---
_id: '14661'
abstract:
- lang: eng
text: 'This paper is concerned with equilibrium configurations of one-dimensional
particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour
interactions and its passage to the continuum. The goal is to derive compactness
results for a Γ-development of the energy with the novelty that external forces
are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates
and thus may model dead as well as live loads. Our result is based on a new technique
for deriving compactness results which are required for calculating the first-order
Γ-limit in the presence of external forces: instead of comparing a configuration
of n atoms to a global minimizer of the Γ-limit, we compare the configuration
to a minimizer in some subclass of functions which in some sense are "close to"
the configuration. The paper is complemented with the study of the minimizers
of the Γ-limit.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marcello
full_name: Carioni, Marcello
last_name: Carioni
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Anja
full_name: Schlömerkemper, Anja
last_name: Schlömerkemper
citation:
ama: 'Carioni M, Fischer JL, Schlömerkemper A. External forces in the continuum
limit of discrete systems with non-convex interaction potentials: Compactness
for a Γ-development. Journal of Convex Analysis. 2023;30(1):217-247.'
apa: 'Carioni, M., Fischer, J. L., & Schlömerkemper, A. (2023). External forces
in the continuum limit of discrete systems with non-convex interaction potentials:
Compactness for a Γ-development. Journal of Convex Analysis. Heldermann
Verlag.'
chicago: 'Carioni, Marcello, Julian L Fischer, and Anja Schlömerkemper. “External
Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction
Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis.
Heldermann Verlag, 2023.'
ieee: 'M. Carioni, J. L. Fischer, and A. Schlömerkemper, “External forces in the
continuum limit of discrete systems with non-convex interaction potentials: Compactness
for a Γ-development,” Journal of Convex Analysis, vol. 30, no. 1. Heldermann
Verlag, pp. 217–247, 2023.'
ista: 'Carioni M, Fischer JL, Schlömerkemper A. 2023. External forces in the continuum
limit of discrete systems with non-convex interaction potentials: Compactness
for a Γ-development. Journal of Convex Analysis. 30(1), 217–247.'
mla: 'Carioni, Marcello, et al. “External Forces in the Continuum Limit of Discrete
Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.”
Journal of Convex Analysis, vol. 30, no. 1, Heldermann Verlag, 2023, pp.
217–47.'
short: M. Carioni, J.L. Fischer, A. Schlömerkemper, Journal of Convex Analysis 30
(2023) 217–247.
date_created: 2023-12-10T23:00:59Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2024-01-16T12:03:05Z
day: '01'
department:
- _id: JuFi
external_id:
arxiv:
- '1811.09857'
isi:
- '001115503400013'
intvolume: ' 30'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.09857
month: '01'
oa: 1
oa_version: Preprint
page: 217-247
publication: Journal of Convex Analysis
publication_identifier:
eissn:
- 2363-6394
issn:
- 0944-6532
publication_status: published
publisher: Heldermann Verlag
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'External forces in the continuum limit of discrete systems with non-convex
interaction potentials: Compactness for a Γ-development'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2023'
...
---
_id: '10550'
abstract:
- lang: eng
text: The global existence of renormalised solutions and convergence to equilibrium
for reaction-diffusion systems with non-linear diffusion are investigated. The
system is assumed to have quasi-positive non-linearities and to satisfy an entropy
inequality. The difficulties in establishing global renormalised solutions caused
by possibly degenerate diffusion are overcome by introducing a new class of weighted
truncation functions. By means of the obtained global renormalised solutions,
we study the large-time behaviour of complex balanced systems arising from chemical
reaction network theory with non-linear diffusion. When the reaction network does
not admit boundary equilibria, the complex balanced equilibrium is shown, by using
the entropy method, to exponentially attract all renormalised solutions in the
same compatibility class. This convergence extends even to a range of non-linear
diffusion, where global existence is an open problem, yet we are able to show
that solutions to approximate systems converge exponentially to equilibrium uniformly
in the regularisation parameter.
acknowledgement: "We thank the referees for their valuable comments and suggestions.
A major part of this work was carried out when B. Q. Tang visited the Institute
of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged.
This work was partially supported by NAWI Graz.\r\nOpen access funding provided
by University of Graz."
article_number: '66'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Klemens
full_name: Fellner, Klemens
last_name: Fellner
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
- first_name: Bao Quoc
full_name: Tang, Bao Quoc
last_name: Tang
citation:
ama: Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and
equilibration of reaction-diffusion systems with non-linear diffusion. Journal
of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w
apa: Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised
solutions and equilibration of reaction-diffusion systems with non-linear diffusion.
Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w
chicago: Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang.
“Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems
with Non-Linear Diffusion.” Journal of Nonlinear Science. Springer Nature,
2023. https://doi.org/10.1007/s00332-023-09926-w.
ieee: K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised
solutions and equilibration of reaction-diffusion systems with non-linear diffusion,”
Journal of Nonlinear Science, vol. 33. Springer Nature, 2023.
ista: Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions
and equilibration of reaction-diffusion systems with non-linear diffusion. Journal
of Nonlinear Science. 33, 66.
mla: Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of
Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear
Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w.
short: K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science
33 (2023).
date_created: 2021-12-16T12:15:35Z
date_published: 2023-06-07T00:00:00Z
date_updated: 2023-08-01T14:40:33Z
day: '07'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00332-023-09926-w
external_id:
arxiv:
- '2109.12019'
isi:
- '001002343400002'
file:
- access_level: open_access
checksum: f3f0f0886098e31c81116cff8183750b
content_type: application/pdf
creator: dernst
date_created: 2023-06-19T07:33:53Z
date_updated: 2023-06-19T07:33:53Z
file_id: '13149'
file_name: 2023_JourNonlinearScience_Fellner.pdf
file_size: 742315
relation: main_file
success: 1
file_date_updated: 2023-06-19T07:33:53Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Nonlinear Science
publication_identifier:
eissn:
- 1432-1467
issn:
- 0938-8974
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global renormalised solutions and equilibration of reaction-diffusion systems
with non-linear diffusion
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2023'
...
---
_id: '10551'
abstract:
- lang: eng
text: 'The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of
fluctuating hydrodynamics; it has been proposed in the physics literature to describe
the fluctuations of the density of N independent diffusing particles in the regime
of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation
presents a substantial challenge for both its analysis and its rigorous mathematical
justification. Besides being non-renormalisable by the theory of regularity structures
by Hairer et al., it has recently been shown to not even admit nontrivial martingale
solutions. In the present work, we give a rigorous and fully quantitative justification
of the Dean–Kawasaki equation by considering the natural regularisation provided
by standard numerical discretisations: We show that structure-preserving discretisations
of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting
diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In
other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate
and efficient numerical simulations of the density fluctuations of independent
diffusing particles.'
acknowledgement: "We thank the anonymous referee for his/her careful reading of the
manuscript and valuable suggestions. FC gratefully acknowledges funding from the
Austrian Science Fund (FWF) through the project F65, and from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science
Fund (FWF)."
article_number: '76'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density
fluctuations in systems of diffusing particles. Archive for Rational Mechanics
and Analysis. 2023;247(5). doi:10.1007/s00205-023-01903-7
apa: Cornalba, F., & Fischer, J. L. (2023). The Dean-Kawasaki equation and the
structure of density fluctuations in systems of diffusing particles. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01903-7
chicago: Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and
the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01903-7.
ieee: F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure
of density fluctuations in systems of diffusing particles,” Archive for Rational
Mechanics and Analysis, vol. 247, no. 5. Springer Nature, 2023.
ista: Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure
of density fluctuations in systems of diffusing particles. Archive for Rational
Mechanics and Analysis. 247(5), 76.
mla: Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and
the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive
for Rational Mechanics and Analysis, vol. 247, no. 5, 76, Springer Nature,
2023, doi:10.1007/s00205-023-01903-7.
short: F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247
(2023).
date_created: 2021-12-16T12:16:03Z
date_published: 2023-08-04T00:00:00Z
date_updated: 2024-01-30T12:10:10Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00205-023-01903-7
ec_funded: 1
external_id:
arxiv:
- '2109.06500'
isi:
- '001043086800001'
file:
- access_level: open_access
checksum: 4529eeff170b6745a461d397ee611b5a
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:09:34Z
date_updated: 2024-01-30T12:09:34Z
file_id: '14904'
file_name: 2023_ArchiveRationalMech_Cornalba.pdf
file_size: 1851185
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:09:34Z
has_accepted_license: '1'
intvolume: ' 247'
isi: 1
issue: '5'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dean-Kawasaki equation and the structure of density fluctuations in systems
of diffusing particles
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 247
year: '2023'
...
---
_id: '14597'
abstract:
- lang: eng
text: "Phase-field models such as the Allen-Cahn equation may give rise to the formation
and evolution of geometric shapes, a phenomenon that may be analyzed rigorously
in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn
equation with a potential with N≥3 distinct minima has been conjectured to describe
the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn
the present work, we give a rigorous proof for this statement in two and three
ambient dimensions and for a suitable class of potentials: As long as a strong
solution to multiphase mean curvature flow exists, solutions to the vectorial
Allen-Cahn equation with well-prepared initial data converge towards multiphase
mean curvature flow in the limit of vanishing interface width parameter ε↘0. We
even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the
gradient flow structure of the Allen-Cahn equation and its limiting motion: Building
on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature
flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation
with multi-well potential. This enables us to overcome the limitations of other
approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn
operator or additional convergence hypotheses for the energy at positive times."
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn
equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143
apa: Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the
vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv.
https://doi.org/10.48550/ARXIV.2203.17143
chicago: Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the
Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv,
n.d. https://doi.org/10.48550/ARXIV.2203.17143.
ieee: J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial
Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. .
ista: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn
equation towards multiphase mean curvature flow. arXiv, 10.48550/ARXIV.2203.17143.
mla: Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial
Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, doi:10.48550/ARXIV.2203.17143.
short: J.L. Fischer, A. Marveggio, ArXiv (n.d.).
date_created: 2023-11-23T09:30:02Z
date_published: 2022-03-31T00:00:00Z
date_updated: 2023-11-30T13:25:02Z
day: '31'
department:
- _id: JuFi
doi: 10.48550/ARXIV.2203.17143
ec_funded: 1
external_id:
arxiv:
- '2203.17143'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2203.17143
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '14587'
relation: dissertation_contains
status: public
status: public
title: Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase
mean curvature flow
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2022'
...
---
_id: '10547'
abstract:
- lang: eng
text: "We establish global-in-time existence results for thermodynamically consistent
reaction-(cross-)diffusion systems coupled to an equation describing heat transfer.
Our main interest is to model species-dependent diffusivities,\r\nwhile at the
same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal
case lies in the intrinsic presence of cross-diffusion type phenomena like the
Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic
equilibria, a nonvanishing temperature gradient may drive a concentration flux
even in a situation with constant concentrations; likewise, a nonvanishing concentration
gradient may drive a heat flux even in a case of spatially constant temperature.
We use time discretisation and regularisation techniques and derive a priori estimates
based on a suitable entropy and the associated entropy production. Renormalised
solutions are used in cases where non-integrable diffusion fluxes or reaction
terms appear."
acknowledgement: M.K. gratefully acknowledges the hospitality of WIAS Berlin, where
a major part of the project was carried out. The research stay of M.K. at WIAS Berlin
was funded by the Austrian Federal Ministry of Education, Science and Research through
a research fellowship for graduates of a promotio sub auspiciis. The research of
A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through
the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems”
(Project no. 235221301), Subproject C05 “Effective models for materials and interfaces
with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin
Schrödinger Institute in Vienna, where some ideas for this work have been developed.
The authors are grateful to two anonymous referees for several helpful comments,
in particular for the short proof of estimate (2.7).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Katharina
full_name: Hopf, Katharina
last_name: Hopf
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
- first_name: Alexander
full_name: Mielke, Alexander
last_name: Mielke
citation:
ama: Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion
systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237
apa: Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence
analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237
chicago: Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke.
“Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics,
2022. https://doi.org/10.1137/20M1387237.
ieee: J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis
of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis,
vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022.
ista: Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of
energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1),
220–267.
mla: Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion
Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society
for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237.
short: J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical
Analysis 54 (2022) 220–267.
date_created: 2021-12-16T12:08:56Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2023-08-02T13:37:03Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/20M1387237
external_id:
arxiv:
- '2012.03792 '
isi:
- '000762768000006'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Energy-Reaction-Diffusion Systems
- Cross Diffusion
- Global-In-Time Existence of Weak/Renormalised Solutions
- Entropy Method
- Onsager System
- Soret/Dufour Effect
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.03792
month: '01'
oa: 1
oa_version: Preprint
page: 220-267
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global existence analysis of energy-reaction-diffusion systems
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '10548'
abstract:
- lang: eng
text: "Consider a linear elliptic partial differential equation in divergence form
with a random coefficient field. The solution operator displays fluctuations around
its expectation. The recently developed pathwise theory of fluctuations in stochastic
homogenization reduces the characterization of these fluctuations to those of
the so-called standard homogenization commutator. In this contribution, we investigate
the scaling limit of this key quantity: starting\r\nfrom a Gaussian-like coefficient
field with possibly strong correlations, we establish the convergence of the rescaled
commutator to a fractional Gaussian field, depending on the decay of correlations
of the coefficient field, and we\r\ninvestigate the (non)degeneracy of the limit.
This extends to general dimension $d\\ge1$ previous results so far limited to
dimension $d=1$, and to the continuum setting with strong correlations recent
results in the discrete iid case."
acknowledgement: The authors thank Ivan Nourdin and Felix Otto for inspiring discussions.
The work of MD is financially supported by the CNRS-Momentum program. Financial
support of AG is acknowledged from the European Research Council under the European
Community’s Seventh Framework Programme (FP7/2014-2019 Grant Agreement QUANTHOM
335410).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mitia
full_name: Duerinckx, Mitia
last_name: Duerinckx
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Antoine
full_name: Gloria, Antoine
last_name: Gloria
citation:
ama: Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator
for Gaussian coefficient fields. Annals of applied probability. 2022;32(2):1179-1209.
doi:10.1214/21-AAP1705
apa: Duerinckx, M., Fischer, J. L., & Gloria, A. (2022). Scaling limit of the
homogenization commutator for Gaussian coefficient fields. Annals of Applied
Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AAP1705
chicago: Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit
of the Homogenization Commutator for Gaussian Coefficient Fields.” Annals
of Applied Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AAP1705.
ieee: M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization
commutator for Gaussian coefficient fields,” Annals of applied probability,
vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022.
ista: Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization
commutator for Gaussian coefficient fields. Annals of applied probability. 32(2),
1179–1209.
mla: Duerinckx, Mitia, et al. “Scaling Limit of the Homogenization Commutator for
Gaussian Coefficient Fields.” Annals of Applied Probability, vol. 32,
no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:10.1214/21-AAP1705.
short: M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022)
1179–1209.
date_created: 2021-12-16T12:10:16Z
date_published: 2022-04-28T00:00:00Z
date_updated: 2023-08-02T13:35:06Z
day: '28'
department:
- _id: JuFi
doi: 10.1214/21-AAP1705
external_id:
arxiv:
- '1910.04088'
isi:
- '000791003700011'
intvolume: ' 32'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.04088
month: '04'
oa: 1
oa_version: Preprint
page: 1179-1209
publication: Annals of applied probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limit of the homogenization commutator for Gaussian coefficient fields
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 32
year: '2022'
...
---
_id: '12304'
abstract:
- lang: eng
text: 'We establish sharp criteria for the instantaneous propagation of free boundaries
in solutions to the thin-film equation. The criteria are formulated in terms of
the initial distribution of mass (as opposed to previous almost-optimal results),
reflecting the fact that mass is a locally conserved quantity for the thin-film
equation. In the regime of weak slippage, our criteria are at the same time necessary
and sufficient. The proof of our upper bounds on free boundary propagation is
based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial
scales: We combine estimates on the local mass and estimates on energies to show
that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially
smaller space-time cylinder with the same time horizon. The derivation of our
lower bounds on free boundary propagation is based on a combination of a monotone
quantity and almost optimal estimates established previously by the second author
with a new estimate connecting motion of mass to entropy production.'
acknowledgement: N. De Nitti acknowledges the kind hospitality of IST Austria within
the framework of the ISTernship Summer Program 2018, during which most of the present
article was written. N. DeNitti has received funding by The Austrian Agency for
International Cooperation in Education &Research (OeAD-GmbH) via its financial support
of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe
Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco
Maddalena for several helpful conversations on topics related to this work.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicola
full_name: De Nitti, Nicola
last_name: De Nitti
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions
to the thin-film equation. Communications in Partial Differential Equations.
2022;47(7):1394-1434. doi:10.1080/03605302.2022.2056702
apa: De Nitti, N., & Fischer, J. L. (2022). Sharp criteria for the waiting time
phenomenon in solutions to the thin-film equation. Communications in Partial
Differential Equations. Taylor & Francis. https://doi.org/10.1080/03605302.2022.2056702
chicago: De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting
Time Phenomenon in Solutions to the Thin-Film Equation.” Communications in
Partial Differential Equations. Taylor & Francis, 2022. https://doi.org/10.1080/03605302.2022.2056702.
ieee: N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation,” Communications in Partial Differential
Equations, vol. 47, no. 7. Taylor & Francis, pp. 1394–1434, 2022.
ista: De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation. Communications in Partial Differential
Equations. 47(7), 1394–1434.
mla: De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time
Phenomenon in Solutions to the Thin-Film Equation.” Communications in Partial
Differential Equations, vol. 47, no. 7, Taylor & Francis, 2022, pp. 1394–434,
doi:10.1080/03605302.2022.2056702.
short: N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations
47 (2022) 1394–1434.
date_created: 2023-01-16T10:06:50Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-04T10:34:31Z
day: '01'
department:
- _id: JuFi
doi: 10.1080/03605302.2022.2056702
external_id:
arxiv:
- '1907.05342'
isi:
- '000805689800001'
intvolume: ' 47'
isi: 1
issue: '7'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1907.05342'
month: '07'
oa: 1
oa_version: Preprint
page: 1394-1434
publication: Communications in Partial Differential Equations
publication_identifier:
eissn:
- 1532-4133
issn:
- 0360-5302
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp criteria for the waiting time phenomenon in solutions to the thin-film
equation
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2022'
...
---
_id: '9335'
abstract:
- lang: eng
text: 'Various degenerate diffusion equations exhibit a waiting time phenomenon:
depending on the “flatness” of the compactly supported initial datum at the boundary
of the support, the support of the solution may not expand for a certain amount
of time. We show that this phenomenon is captured by particular Lagrangian discretizations
of the porous medium and the thin film equations, and we obtain sufficient criteria
for the occurrence of waiting times that are consistent with the known ones for
the original PDEs. For the spatially discrete solution, the waiting time phenomenon
refers to a deviation of the edge of support from its original position by a quantity
comparable to the mesh width, over a mesh-independent time interval. Our proof
is based on estimates on the fluid velocity in Lagrangian coordinates. Combining
weighted entropy estimates with an iteration technique à la Stampacchia leads
to upper bounds on free boundary propagation. Numerical simulations show that
the phenomenon is already clearly visible for relatively coarse discretizations.'
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109, “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Daniel
full_name: Matthes, Daniel
last_name: Matthes
citation:
ama: Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis.
2021;59(1):60-87. doi:10.1137/19M1300017
apa: Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially
discretized porous medium and thin film equations. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017
chicago: Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in
Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal
on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1300017.
ieee: J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized
porous medium and thin film equations,” SIAM Journal on Numerical Analysis,
vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021.
ista: Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1),
60–87.
mla: Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially
Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical
Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics,
2021, pp. 60–87, doi:10.1137/19M1300017.
short: J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87.
date_created: 2021-04-18T22:01:42Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-08T13:10:40Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/19M1300017
external_id:
arxiv:
- '1911.04185'
isi:
- '000625044600003'
intvolume: ' 59'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1911.04185
month: '01'
oa: 1
oa_version: Preprint
page: 60-87
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The waiting time phenomenon in spatially discretized porous medium and thin
film equations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...
---
_id: '9352'
abstract:
- lang: eng
text: This paper provides an a priori error analysis of a localized orthogonal decomposition
method for the numerical stochastic homogenization of a model random diffusion
problem. If the uniformly elliptic and bounded random coefficient field of the
model problem is stationary and satisfies a quantitative decorrelation assumption
in the form of the spectral gap inequality, then the expected $L^2$ error of the
method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$,
$\varepsilon$ being the small correlation length of the random coefficient and
$H$ the width of the coarse finite element mesh that determines the spatial resolution.
The proof bridges recent results of numerical homogenization and quantitative
stochastic homogenization.
acknowledgement: 'This work was initiated while the authors enjoyed the kind hospitality
of the Hausdorff Institute for Mathematics in Bonn during the trimester program
Multiscale Problems: Algorithms, Numerical Analysis, and Computation. D. Peterseim
would like to acknowledge the kind hospitality of the Erwin Schrödinger International
Institute for Mathematics and Physics (ESI), where parts of this research were
developed under the frame of the thematic program Numerical Analysis of Complex
PDE Models in the Sciences.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Dietmar
full_name: Gallistl, Dietmar
last_name: Gallistl
- first_name: Dietmar
full_name: Peterseim, Dietmar
last_name: Peterseim
citation:
ama: Fischer JL, Gallistl D, Peterseim D. A priori error analysis of a numerical
stochastic homogenization method. SIAM Journal on Numerical Analysis. 2021;59(2):660-674.
doi:10.1137/19M1308992
apa: Fischer, J. L., Gallistl, D., & Peterseim, D. (2021). A priori error analysis
of a numerical stochastic homogenization method. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1308992
chicago: Fischer, Julian L, Dietmar Gallistl, and Dietmar Peterseim. “A Priori Error
Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1308992.
ieee: J. L. Fischer, D. Gallistl, and D. Peterseim, “A priori error analysis of
a numerical stochastic homogenization method,” SIAM Journal on Numerical Analysis,
vol. 59, no. 2. Society for Industrial and Applied Mathematics, pp. 660–674, 2021.
ista: Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical
stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674.
mla: Fischer, Julian L., et al. “A Priori Error Analysis of a Numerical Stochastic
Homogenization Method.” SIAM Journal on Numerical Analysis, vol. 59, no.
2, Society for Industrial and Applied Mathematics, 2021, pp. 660–74, doi:10.1137/19M1308992.
short: J.L. Fischer, D. Gallistl, D. Peterseim, SIAM Journal on Numerical Analysis
59 (2021) 660–674.
date_created: 2021-04-25T22:01:31Z
date_published: 2021-03-09T00:00:00Z
date_updated: 2023-08-08T13:13:37Z
day: '09'
department:
- _id: JuFi
doi: 10.1137/19M1308992
external_id:
arxiv:
- '1912.11646'
isi:
- '000646030400003'
intvolume: ' 59'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.11646
month: '03'
oa: 1
oa_version: Preprint
page: 660-674
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A priori error analysis of a numerical stochastic homogenization method
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...
---
_id: '10549'
abstract:
- lang: eng
text: We derive optimal-order homogenization rates for random nonlinear elliptic
PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely,
for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially
homogeneous statistics) and fast decay of correlations on scales larger than the
microscale \varepsilon >0, we establish homogenization error estimates of the
order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon
|^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have
been limited to a small algebraic rate of convergence \varepsilon ^\delta . We
also establish error estimates for the approximation of the homogenized operator
by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for
a representative volume of size L. Our results also hold in the case of systems
for which a (small-scale) C^{1,\alpha } regularity theory is available.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) – project number 405009441.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Stefan
full_name: Neukamm, Stefan
last_name: Neukamm
citation:
ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational
Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9
apa: Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9
chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in
Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.”
Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9.
ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems,” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp.
343–452, 2021.
ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics
and Analysis. 242(1), 343–452.
mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic
Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021,
pp. 343–452, doi:10.1007/s00205-021-01686-9.
short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242
(2021) 343–452.
date_created: 2021-12-16T12:12:33Z
date_published: 2021-06-30T00:00:00Z
date_updated: 2023-08-17T06:23:21Z
day: '30'
ddc:
- '530'
department:
- _id: JuFi
doi: 10.1007/s00205-021-01686-9
external_id:
arxiv:
- '1908.02273'
isi:
- '000668431200001'
file:
- access_level: open_access
checksum: cc830b739aed83ca2e32c4e0ce266a4c
content_type: application/pdf
creator: cchlebak
date_created: 2021-12-16T14:58:08Z
date_updated: 2021-12-16T14:58:08Z
file_id: '10558'
file_name: 2021_ArchRatMechAnalysis_Fischer.pdf
file_size: 1640121
relation: main_file
success: 1
file_date_updated: 2021-12-16T14:58:08Z
has_accepted_license: '1'
intvolume: ' 242'
isi: 1
issue: '1'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 343-452
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly
elliptic equations and systems
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 242
year: '2021'
...
---
_id: '8697'
abstract:
- lang: eng
text: In the computation of the material properties of random alloys, the method
of 'special quasirandom structures' attempts to approximate the properties of
the alloy on a finite volume with higher accuracy by replicating certain statistics
of the random atomic lattice in the finite volume as accurately as possible. In
the present work, we provide a rigorous justification for a variant of this method
in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach
is based on a recent analysis of a related variance reduction method in stochastic
homogenization of linear elliptic PDEs and the locality properties of the TFW
model. Concerning the latter, we extend an exponential locality result by Nazar
and Ortner to include point charges, a result that may be of independent interest.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Fischer JL, Kniely M. Variance reduction for effective energies of random lattices
in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772.
doi:10.1088/1361-6544/ab9728
apa: Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies
of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity.
IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728
chicago: Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective
Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity.
IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728.
ieee: J. L. Fischer and M. Kniely, “Variance reduction for effective energies of
random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity,
vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.
ista: Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random
lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.
mla: Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies
of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity,
vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728.
short: J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.
date_created: 2020-10-25T23:01:16Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-08-22T10:38:38Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab9728
external_id:
arxiv:
- '1906.12245'
isi:
- '000576492700001'
file:
- access_level: open_access
checksum: ed90bc6eb5f32ee6157fef7f3aabc057
content_type: application/pdf
creator: cziletti
date_created: 2020-10-27T12:09:57Z
date_updated: 2020-10-27T12:09:57Z
file_id: '8710'
file_name: 2020_Nonlinearity_Fischer.pdf
file_size: 1223899
relation: main_file
success: 1
file_date_updated: 2020-10-27T12:09:57Z
has_accepted_license: '1'
intvolume: ' 33'
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issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 5733-5772
publication: Nonlinearity
publication_identifier:
eissn:
- '13616544'
issn:
- '09517715'
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von
Weizsäcker model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2020'
...
---
_id: '7489'
abstract:
- lang: eng
text: 'In the present work, we consider the evolution of two fluids separated by
a sharp interface in the presence of surface tension—like, for example, the evolution
of oil bubbles in water. Our main result is a weak–strong uniqueness principle
for the corresponding free boundary problem for the incompressible Navier–Stokes
equation: as long as a strong solution exists, any varifold solution must coincide
with it. In particular, in the absence of physical singularities, the concept
of varifold solutions—whose global in time existence has been shown by Abels (Interfaces
Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism
for non-uniqueness. The key ingredient of our approach is the construction of
a relative entropy functional capable of controlling the interface error. If the
viscosities of the two fluids do not coincide, even for classical (strong) solutions
the gradient of the velocity field becomes discontinuous at the interface, introducing
the need for a careful additional adaption of the relative entropy.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation
for two fluids with surface tension. Archive for Rational Mechanics and Analysis.
2020;236:967-1087. doi:10.1007/s00205-019-01486-2
apa: Fischer, J. L., & Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes
equation for two fluids with surface tension. Archive for Rational Mechanics
and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01486-2
chicago: Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Surface Tension.” Archive for Rational
Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-019-01486-2.
ieee: J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes
equation for two fluids with surface tension,” Archive for Rational Mechanics
and Analysis, vol. 236. Springer Nature, pp. 967–1087, 2020.
ista: Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation
for two fluids with surface tension. Archive for Rational Mechanics and Analysis.
236, 967–1087.
mla: Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Surface Tension.” Archive for Rational Mechanics
and Analysis, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:10.1007/s00205-019-01486-2.
short: J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236
(2020) 967–1087.
date_created: 2020-02-16T23:00:50Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '01'
ddc:
- '530'
- '532'
department:
- _id: JuFi
doi: 10.1007/s00205-019-01486-2
ec_funded: 1
external_id:
isi:
- '000511060200001'
file:
- access_level: open_access
checksum: f107e21b58f5930876f47144be37cf6c
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T09:14:22Z
date_updated: 2020-11-20T09:14:22Z
file_id: '8779'
file_name: 2020_ArchRatMechAn_Fischer.pdf
file_size: 1897571
relation: main_file
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intvolume: ' 236'
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language:
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oa: 1
oa_version: Published Version
page: 967-1087
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call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
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issn:
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publisher: Springer Nature
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface
tension
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 236
year: '2020'
...
---
_id: '9039'
abstract:
- lang: eng
text: We give a short and self-contained proof for rates of convergence of the Allen--Cahn
equation towards mean curvature flow, assuming that a classical (smooth) solution
to the latter exists and starting from well-prepared initial data. Our approach
is based on a relative entropy technique. In particular, it does not require a
stability analysis for the linearized Allen--Cahn operator. As our analysis also
does not rely on the comparison principle, we expect it to be applicable to more
complex equations and systems.
acknowledgement: "This work was supported by the European Union's Horizon 2020 Research
and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385
and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation)
under Germany's Excellence Strategy, EXC-2047/1--390685813."
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Theresa M.
full_name: Simon, Theresa M.
last_name: Simon
citation:
ama: 'Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182'
apa: 'Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of
the Allen-Cahn equation to mean curvature flow: A short proof based on relative
entropies. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/20M1322182'
chicago: 'Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates
of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative
Entropies.” SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182.'
ieee: 'J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn
equation to mean curvature flow: A short proof based on relative entropies,” SIAM
Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and
Applied Mathematics, pp. 6222–6233, 2020.'
ista: 'Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 52(6), 6222–6233.'
mla: 'Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to
Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal
on Mathematical Analysis, vol. 52, no. 6, Society for Industrial and Applied
Mathematics, 2020, pp. 6222–33, doi:10.1137/20M1322182.'
short: J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis
52 (2020) 6222–6233.
date_created: 2021-01-24T23:01:09Z
date_published: 2020-12-15T00:00:00Z
date_updated: 2023-08-24T11:15:16Z
day: '15'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/20M1322182
ec_funded: 1
external_id:
isi:
- '000600695200027'
file:
- access_level: open_access
checksum: 21aa1cf4c30a86a00cae15a984819b5d
content_type: application/pdf
creator: dernst
date_created: 2021-01-25T07:48:39Z
date_updated: 2021-01-25T07:48:39Z
file_id: '9041'
file_name: 2020_SIAM_Fischer.pdf
file_size: 310655
relation: main_file
success: 1
file_date_updated: 2021-01-25T07:48:39Z
has_accepted_license: '1'
intvolume: ' 52'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 6222-6233
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- '10957154'
issn:
- '00361410'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates of the Allen-Cahn equation to mean curvature flow: A short
proof based on relative entropies'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 52
year: '2020'
...
---
_id: '10012'
abstract:
- lang: eng
text: We prove that in the absence of topological changes, the notion of BV solutions
to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical)
non-uniqueness. Our approach is based on the local structure of the energy landscape
near a classical evolution by mean curvature. Mean curvature flow being the gradient
flow of the surface energy functional, we develop a gradient-flow analogue of
the notion of calibrations. Just like the existence of a calibration guarantees
that one has reached a global minimum in the energy landscape, the existence of
a "gradient flow calibration" ensures that the route of steepest descent in the
energy landscape is unique and stable.
acknowledgement: Parts of the paper were written during the visit of the authors to
the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the
framework of the trimester program “Evolution of Interfaces”. The support and the
hospitality of HIM are gratefully acknowledged. This project has received funding
from the European Union’s Horizon 2020 research and innovation programme under the
Marie Sklodowska-Curie Grant Agreement No. 665385.
article_number: '2003.05478'
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Thilo
full_name: Simon, Thilo
last_name: Simon
citation:
ama: 'Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape
in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions.
arXiv.'
apa: 'Fischer, J. L., Hensel, S., Laux, T., & Simon, T. (n.d.). The local structure
of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness
and stability of evolutions. arXiv.'
chicago: 'Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local
Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong
Uniqueness and Stability of Evolutions.” ArXiv, n.d.'
ieee: 'J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of
the energy landscape in multiphase mean curvature flow: weak-strong uniqueness
and stability of evolutions,” arXiv. .'
ista: 'Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy
landscape in multiphase mean curvature flow: weak-strong uniqueness and stability
of evolutions. arXiv, 2003.05478.'
mla: 'Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in
Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.”
ArXiv, 2003.05478.'
short: J.L. Fischer, S. Hensel, T. Laux, T. Simon, ArXiv (n.d.).
date_created: 2021-09-13T12:17:11Z
date_published: 2020-03-11T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '11'
department:
- _id: JuFi
ec_funded: 1
external_id:
arxiv:
- '2003.05478'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.05478
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '10007'
relation: dissertation_contains
status: public
status: public
title: 'The local structure of the energy landscape in multiphase mean curvature flow:
weak-strong uniqueness and stability of evolutions'
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '6617'
abstract:
- lang: eng
text: 'The effective large-scale properties of materials with random heterogeneities
on a small scale are typically determined by the method of representative volumes:
a sample of the random material is chosen—the representative volume—and its effective
properties are computed by the cell formula. Intuitively, for a fixed sample size
it should be possible to increase the accuracy of the method by choosing a material
sample which captures the statistical properties of the material particularly
well; for example, for a composite material consisting of two constituents, one
would select a representative volume in which the volume fraction of the constituents
matches closely with their volume fraction in the overall material. Inspired by
similar attempts in materials science, Le Bris, Legoll and Minvielle have designed
a selection approach for representative volumes which performs remarkably well
in numerical examples of linear materials with moderate contrast. In the present
work, we provide a rigorous analysis of this selection approach for representative
volumes in the context of stochastic homogenization of linear elliptic equations.
In particular, we prove that the method essentially never performs worse than
a random selection of the material sample and may perform much better if the selection
criterion for the material samples is chosen suitably.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Fischer JL. The choice of representative volumes in the approximation of effective
properties of random materials. Archive for Rational Mechanics and Analysis.
2019;234(2):635–726. doi:10.1007/s00205-019-01400-w
apa: Fischer, J. L. (2019). The choice of representative volumes in the approximation
of effective properties of random materials. Archive for Rational Mechanics
and Analysis. Springer. https://doi.org/10.1007/s00205-019-01400-w
chicago: Fischer, Julian L. “The Choice of Representative Volumes in the Approximation
of Effective Properties of Random Materials.” Archive for Rational Mechanics
and Analysis. Springer, 2019. https://doi.org/10.1007/s00205-019-01400-w.
ieee: J. L. Fischer, “The choice of representative volumes in the approximation
of effective properties of random materials,” Archive for Rational Mechanics
and Analysis, vol. 234, no. 2. Springer, pp. 635–726, 2019.
ista: Fischer JL. 2019. The choice of representative volumes in the approximation
of effective properties of random materials. Archive for Rational Mechanics and
Analysis. 234(2), 635–726.
mla: Fischer, Julian L. “The Choice of Representative Volumes in the Approximation
of Effective Properties of Random Materials.” Archive for Rational Mechanics
and Analysis, vol. 234, no. 2, Springer, 2019, pp. 635–726, doi:10.1007/s00205-019-01400-w.
short: J.L. Fischer, Archive for Rational Mechanics and Analysis 234 (2019) 635–726.
date_created: 2019-07-07T21:59:23Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-08-28T12:31:21Z
day: '01'
ddc:
- '500'
department:
- _id: JuFi
doi: 10.1007/s00205-019-01400-w
external_id:
arxiv:
- '1807.00834'
isi:
- '000482386000006'
file:
- access_level: open_access
checksum: 4cff75fa6addb0770991ad9c474ab404
content_type: application/pdf
creator: kschuh
date_created: 2019-07-08T15:56:47Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6626'
file_name: Springer_2019_Fischer.pdf
file_size: 1377659
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: ' 234'
isi: 1
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 635–726
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: The choice of representative volumes in the approximation of effective properties
of random materials
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 234
year: '2019'
...
---
_id: '151'
abstract:
- lang: eng
text: We construct planar bi-Sobolev mappings whose local volume distortion is bounded
from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2
we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞,
we provide bi-Lipschitz maps. The basic building block of our construction are
bi-Lipschitz maps which stretch a given compact subset of the unit square by a
given factor while preserving the boundary. The construction of these stretching
maps relies on a slight strengthening of the celebrated covering result of Alberti,
Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We
apply our result to a model functional in nonlinear elasticity, the integrand
of which features fast blowup as the Jacobian determinant of the deformation becomes
small. For such functionals, the derivation of the equilibrium equations for minimizers
requires an additional regularization of test functions, which our maps provide.
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Olivier
full_name: Kneuss, Olivier
last_name: Kneuss
citation:
ama: Fischer JL, Kneuss O. Bi-Sobolev solutions to the prescribed Jacobian inequality
in the plane with L p data and applications to nonlinear elasticity. Journal
of Differential Equations. 2019;266(1):257-311. doi:10.1016/j.jde.2018.07.045
apa: Fischer, J. L., & Kneuss, O. (2019). Bi-Sobolev solutions to the prescribed
Jacobian inequality in the plane with L p data and applications to nonlinear elasticity.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2018.07.045
chicago: Fischer, Julian L, and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed
Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.”
Journal of Differential Equations. Elsevier, 2019. https://doi.org/10.1016/j.jde.2018.07.045.
ieee: J. L. Fischer and O. Kneuss, “Bi-Sobolev solutions to the prescribed Jacobian
inequality in the plane with L p data and applications to nonlinear elasticity,”
Journal of Differential Equations, vol. 266, no. 1. Elsevier, pp. 257–311,
2019.
ista: Fischer JL, Kneuss O. 2019. Bi-Sobolev solutions to the prescribed Jacobian
inequality in the plane with L p data and applications to nonlinear elasticity.
Journal of Differential Equations. 266(1), 257–311.
mla: Fischer, Julian L., and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed
Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.”
Journal of Differential Equations, vol. 266, no. 1, Elsevier, 2019, pp.
257–311, doi:10.1016/j.jde.2018.07.045.
short: J.L. Fischer, O. Kneuss, Journal of Differential Equations 266 (2019) 257–311.
date_created: 2018-12-11T11:44:54Z
date_published: 2019-01-05T00:00:00Z
date_updated: 2023-09-08T13:25:35Z
day: '05'
department:
- _id: JuFi
doi: 10.1016/j.jde.2018.07.045
external_id:
arxiv:
- '1408.1587'
isi:
- '000449108500010'
intvolume: ' 266'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1408.1587
month: '01'
oa: 1
oa_version: Preprint
page: 257 - 311
publication: Journal of Differential Equations
publication_status: published
publisher: Elsevier
publist_id: '7770'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with
L p data and applications to nonlinear elasticity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 266
year: '2019'
...
---
_id: '606'
abstract:
- lang: eng
text: We establish the existence of a global solution for a new family of fluid-like
equations, which are obtained in certain regimes in as the mean-field evolution
of the supercurrent density in a (2D section of a) type-II superconductor with
pinning and with imposed electric current. We also consider general vortex-sheet
initial data, and investigate the uniqueness and regularity properties of the
solution. For some choice of parameters, the equation under investigation coincides
with the so-called lake equation from 2D shallow water fluid dynamics, and our
analysis then leads to a new existence result for rough initial data.
acknowledgement: "The work of the author is supported by F.R.S.-FNRS ( Fonds de la
Recherche Scientifique - FNRS ) through a Research Fellowship.\r\n\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Mitia
full_name: Duerinckx, Mitia
last_name: Duerinckx
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Duerinckx M, Fischer JL. Well-posedness for mean-field evolutions arising in
superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis.
2018;35(5):1267-1319. doi:10.1016/j.anihpc.2017.11.004
apa: Duerinckx, M., & Fischer, J. L. (2018). Well-posedness for mean-field evolutions
arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non
Linear Analysis. Elsevier. https://doi.org/10.1016/j.anihpc.2017.11.004
chicago: Duerinckx, Mitia, and Julian L Fischer. “Well-Posedness for Mean-Field
Evolutions Arising in Superconductivity.” Annales de l’Institut Henri Poincare
(C) Non Linear Analysis. Elsevier, 2018. https://doi.org/10.1016/j.anihpc.2017.11.004.
ieee: M. Duerinckx and J. L. Fischer, “Well-posedness for mean-field evolutions
arising in superconductivity,” Annales de l’Institut Henri Poincare (C) Non
Linear Analysis, vol. 35, no. 5. Elsevier, pp. 1267–1319, 2018.
ista: Duerinckx M, Fischer JL. 2018. Well-posedness for mean-field evolutions arising
in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis.
35(5), 1267–1319.
mla: Duerinckx, Mitia, and Julian L. Fischer. “Well-Posedness for Mean-Field Evolutions
Arising in Superconductivity.” Annales de l’Institut Henri Poincare (C) Non
Linear Analysis, vol. 35, no. 5, Elsevier, 2018, pp. 1267–319, doi:10.1016/j.anihpc.2017.11.004.
short: M. Duerinckx, J.L. Fischer, Annales de l’Institut Henri Poincare (C) Non
Linear Analysis 35 (2018) 1267–1319.
date_created: 2018-12-11T11:47:27Z
date_published: 2018-08-01T00:00:00Z
date_updated: 2023-09-19T10:39:09Z
day: '01'
department:
- _id: JuFi
doi: 10.1016/j.anihpc.2017.11.004
external_id:
arxiv:
- '1607.00268'
isi:
- '000437975500005'
intvolume: ' 35'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1607.00268
month: '08'
oa: 1
oa_version: Submitted Version
page: 1267-1319
publication: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
publication_status: published
publisher: Elsevier
publist_id: '7199'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Well-posedness for mean-field evolutions arising in superconductivity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 35
year: '2018'
...
---
_id: '404'
abstract:
- lang: eng
text: "We construct martingale solutions to stochastic thin-film equations by introducing
a (spatial) semidiscretization and establishing convergence. The discrete scheme
allows for variants of the energy and entropy estimates in the continuous setting
as long as the discrete energy does not exceed certain threshold values depending
on the spatial grid size $h$. Using a stopping time argument to prolongate high-energy
paths constant in time, arbitrary moments of coupled energy/entropy functionals
can be controlled. Having established Hölder regularity of approximate solutions,
the convergence proof is then based on compactness arguments---in particular on
Jakubowski's generalization of Skorokhod's theorem---weak convergence methods,
and recent tools on martingale convergence.\r\n\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Günther
full_name: Grün, Günther
last_name: Grün
citation:
ama: Fischer JL, Grün G. Existence of positive solutions to stochastic thin-film
equations. SIAM Journal on Mathematical Analysis. 2018;50(1):411-455. doi:10.1137/16M1098796
apa: Fischer, J. L., & Grün, G. (2018). Existence of positive solutions to stochastic
thin-film equations. SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics . https://doi.org/10.1137/16M1098796
chicago: Fischer, Julian L, and Günther Grün. “Existence of Positive Solutions to
Stochastic Thin-Film Equations.” SIAM Journal on Mathematical Analysis.
Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1098796.
ieee: J. L. Fischer and G. Grün, “Existence of positive solutions to stochastic
thin-film equations,” SIAM Journal on Mathematical Analysis, vol. 50, no.
1. Society for Industrial and Applied Mathematics , pp. 411–455, 2018.
ista: Fischer JL, Grün G. 2018. Existence of positive solutions to stochastic thin-film
equations. SIAM Journal on Mathematical Analysis. 50(1), 411–455.
mla: Fischer, Julian L., and Günther Grün. “Existence of Positive Solutions to Stochastic
Thin-Film Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no.
1, Society for Industrial and Applied Mathematics , 2018, pp. 411–55, doi:10.1137/16M1098796.
short: J.L. Fischer, G. Grün, SIAM Journal on Mathematical Analysis 50 (2018) 411–455.
date_created: 2018-12-11T11:46:17Z
date_published: 2018-01-30T00:00:00Z
date_updated: 2023-09-11T13:59:22Z
day: '30'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/16M1098796
external_id:
isi:
- '000426630900015'
file:
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checksum: 89a8eae7c52bb356c04f52b44bff4b5a
content_type: application/pdf
creator: dernst
date_created: 2019-11-07T12:20:25Z
date_updated: 2020-07-14T12:46:22Z
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file_name: 2018_SIAM_Fischer.pdf
file_size: 557338
relation: main_file
file_date_updated: 2020-07-14T12:46:22Z
has_accepted_license: '1'
intvolume: ' 50'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 411 - 455
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7425'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Existence of positive solutions to stochastic thin-film equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...
---
_id: '712'
abstract:
- lang: eng
text: 'We establish a weak–strong uniqueness principle for solutions to entropy-dissipating
reaction–diffusion equations: As long as a strong solution to the reaction–diffusion
equation exists, any weak solution and even any renormalized solution must coincide
with this strong solution. Our assumptions on the reaction rates are just the
entropy condition and local Lipschitz continuity; in particular, we do not impose
any growth restrictions on the reaction rates. Therefore, our result applies to
any single reversible reaction with mass-action kinetics as well as to systems
of reversible reactions with mass-action kinetics satisfying the detailed balance
condition. Renormalized solutions are known to exist globally in time for reaction–diffusion
equations with entropy-dissipating reaction rates; in contrast, the global-in-time
existence of weak solutions is in general still an open problem–even for smooth
data–, thereby motivating the study of renormalized solutions. The key ingredient
of our result is a careful adjustment of the usual relative entropy functional,
whose evolution cannot be controlled properly for weak solutions or renormalized
solutions.'
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: 'Fischer JL. Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
equations. Nonlinear Analysis: Theory, Methods and Applications. 2017;159:181-207.
doi:10.1016/j.na.2017.03.001'
apa: 'Fischer, J. L. (2017). Weak–strong uniqueness of solutions to entropy dissipating
reaction–diffusion equations. Nonlinear Analysis: Theory, Methods and Applications.
Elsevier. https://doi.org/10.1016/j.na.2017.03.001'
chicago: 'Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating
Reaction–Diffusion Equations.” Nonlinear Analysis: Theory, Methods and Applications.
Elsevier, 2017. https://doi.org/10.1016/j.na.2017.03.001.'
ieee: 'J. L. Fischer, “Weak–strong uniqueness of solutions to entropy dissipating
reaction–diffusion equations,” Nonlinear Analysis: Theory, Methods and Applications,
vol. 159. Elsevier, pp. 181–207, 2017.'
ista: 'Fischer JL. 2017. Weak–strong uniqueness of solutions to entropy dissipating
reaction–diffusion equations. Nonlinear Analysis: Theory, Methods and Applications.
159, 181–207.'
mla: 'Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating
Reaction–Diffusion Equations.” Nonlinear Analysis: Theory, Methods and Applications,
vol. 159, Elsevier, 2017, pp. 181–207, doi:10.1016/j.na.2017.03.001.'
short: 'J.L. Fischer, Nonlinear Analysis: Theory, Methods and Applications 159 (2017)
181–207.'
date_created: 2018-12-11T11:48:05Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:55Z
day: '01'
department:
- _id: JuFi
doi: 10.1016/j.na.2017.03.001
intvolume: ' 159'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1703.00730
month: '08'
oa: 1
oa_version: Submitted Version
page: 181 - 207
publication: 'Nonlinear Analysis: Theory, Methods and Applications'
publication_identifier:
issn:
- 0362546X
publication_status: published
publisher: Elsevier
publist_id: '6975'
quality_controlled: '1'
scopus_import: 1
status: public
title: Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
equations
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 159
year: '2017'
...
---
_id: '1014'
abstract:
- lang: eng
text: 'We consider the large-scale regularity of solutions to second-order linear
elliptic equations with random coefficient fields. In contrast to previous works
on regularity theory for random elliptic operators, our interest is in the regularity
at the boundary: We consider problems posed on the half-space with homogeneous
Dirichlet boundary conditions and derive an associated C1,α-type large-scale regularity
theory in the form of a corresponding decay estimate for the homogenization-adapted
tilt-excess. This regularity theory entails an associated Liouville-type theorem.
The results are based on the existence of homogenization correctors adapted to
the half-space setting, which we construct-by an entirely deterministic argument-as
a modification of the homogenization corrector on the whole space. This adaption
procedure is carried out inductively on larger scales, crucially relying on the
regularity theory already established on smaller scales.'
article_processing_charge: No
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Claudia
full_name: Raithel, Claudia
last_name: Raithel
citation:
ama: Fischer JL, Raithel C. Liouville principles and a large-scale regularity theory
for random elliptic operators on the half-space. SIAM Journal on Mathematical
Analysis. 2017;49(1):82-114. doi:10.1137/16M1070384
apa: Fischer, J. L., & Raithel, C. (2017). Liouville principles and a large-scale
regularity theory for random elliptic operators on the half-space. SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics .
https://doi.org/10.1137/16M1070384
chicago: Fischer, Julian L, and Claudia Raithel. “Liouville Principles and a Large-Scale
Regularity Theory for Random Elliptic Operators on the Half-Space.” SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics ,
2017. https://doi.org/10.1137/16M1070384.
ieee: J. L. Fischer and C. Raithel, “Liouville principles and a large-scale regularity
theory for random elliptic operators on the half-space,” SIAM Journal on Mathematical
Analysis, vol. 49, no. 1. Society for Industrial and Applied Mathematics ,
pp. 82–114, 2017.
ista: Fischer JL, Raithel C. 2017. Liouville principles and a large-scale regularity
theory for random elliptic operators on the half-space. SIAM Journal on Mathematical
Analysis. 49(1), 82–114.
mla: Fischer, Julian L., and Claudia Raithel. “Liouville Principles and a Large-Scale
Regularity Theory for Random Elliptic Operators on the Half-Space.” SIAM Journal
on Mathematical Analysis, vol. 49, no. 1, Society for Industrial and Applied
Mathematics , 2017, pp. 82–114, doi:10.1137/16M1070384.
short: J.L. Fischer, C. Raithel, SIAM Journal on Mathematical Analysis 49 (2017)
82–114.
date_created: 2018-12-11T11:49:41Z
date_published: 2017-01-12T00:00:00Z
date_updated: 2023-09-22T09:43:36Z
day: '12'
doi: 10.1137/16M1070384
extern: '1'
external_id:
isi:
- '000396681800004'
intvolume: ' 49'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1703.04328
month: '01'
oa: 1
oa_version: Submitted Version
page: 82 - 114
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
issn:
- '00361410'
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '6381'
quality_controlled: '1'
status: public
title: Liouville principles and a large-scale regularity theory for random elliptic
operators on the half-space
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 49
year: '2017'
...