---
_id: '14797'
abstract:
- lang: eng
text: We study a random matching problem on closed compact 2 -dimensional Riemannian
manifolds (with respect to the squared Riemannian distance), with samples of random
points whose common law is absolutely continuous with respect to the volume measure
with strictly positive and bounded density. We show that given two sequences of
numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity,
the optimal transport plan between the two empirical measures μn and νm is
quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear
elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère
equation. This is obtained in the case of samples of correlated random points
for which a stretched exponential decay of the α -mixing coefficient holds and
for a class of discrete-time Markov chains having a unique absolutely continuous
invariant measure with respect to the volume measure.
acknowledgement: "NC has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (Grant
agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems.
FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics
Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute
for Mathematics in the Sciences."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Francesco
full_name: Mattesini, Francesco
last_name: Mattesini
citation:
ama: Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete
random matching problem. Probability Theory and Related Fields. 2024. doi:10.1007/s00440-023-01254-0
apa: Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for
the quadratic 2D-discrete random matching problem. Probability Theory and Related
Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0
chicago: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0.
ieee: N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic
2D-discrete random matching problem,” Probability Theory and Related Fields.
Springer Nature, 2024.
ista: Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic
2D-discrete random matching problem. Probability Theory and Related Fields.
mla: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields, Springer Nature, 2024, doi:10.1007/s00440-023-01254-0.
short: N. Clozeau, F. Mattesini, Probability Theory and Related Fields (2024).
date_created: 2024-01-14T23:00:57Z
date_published: 2024-01-04T00:00:00Z
date_updated: 2025-08-12T12:22:41Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01254-0
ec_funded: 1
external_id:
arxiv:
- '2303.00353'
has_accepted_license: '1'
keyword:
- Troll
- Norway
- Fjell
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00440-023-01254-0
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Annealed quantitative estimates for the quadratic 2D-discrete random matching
problem
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
year: '2024'
...
---
_id: '14587'
abstract:
- lang: eng
text: "This thesis concerns the application of variational methods to the study
of evolution problems arising in fluid mechanics and in material sciences. The
main focus is on weak-strong stability properties of some curvature driven interface
evolution problems, such as the two-phase Navier–Stokes flow with surface tension
and multiphase mean curvature flow, and on the phase-field approximation of the
latter. Furthermore, we discuss a variational approach to the study of a class
of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes
flow with surface tension within a bounded domain. The two fluids are immiscible
and separated by a sharp interface, which intersects the boundary of the domain
at a constant contact angle of ninety degree. We devise a suitable concept of
varifolds solutions for the associated interface evolution problem and we establish
a weak-strong uniqueness principle in case of a two dimensional ambient space.
In order to focus on the boundary effects and on the singular geometry of the
evolving domains, we work for simplicity in the regime of same viscosities for
the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the
convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature
flow for a suitable class of multi- well potentials and for well-prepared initial
data. We even establish a rate of convergence. Our relative energy approach relies
on the concept of gradient-flow calibration for branching singularities in multiphase
mean curvature flow and thus enables us to overcome the limitations of other approaches.
To the best of the author’s knowledge, our result is the first quantitative and
unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis
thesis also contains a first study of weak-strong stability for planar multiphase
mean curvature flow beyond the singularity resulting from a topology change. Previous
weak-strong results are indeed limited to time horizons before the first topology
change of the strong solution. We consider circular topology changes and we prove
weak-strong stability for BV solutions to planar multiphase mean curvature flow
beyond the associated singular times by dynamically adapting the strong solutions
to the weak one by means of a space-time shift.\r\nIn the context of interface
evolution problems, our proofs for the main results of this thesis are based on
the relative energy technique, relying on novel suitable notions of relative energy
functionals, which in particular measure the interface error. Our statements follow
from the resulting stability estimates for the relative energy associated to the
problem.\r\nAt last, we introduce a variational approach to the study of nonlinear
evolution problems. This approach hinges on the minimization of a parameter dependent
family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy
(WIDE) functionals. We consider a class of doubly nonlinear wave equations and
establish the convergence, up to subsequences, of the associated WIDE minimizers
to a solution of the target problem as the parameter goes to zero."
acknowledgement: The research projects contained in this thesis have received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 948819).
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Marveggio A. Weak-strong stability and phase-field approximation of interface
evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587
apa: Marveggio, A. (2023). Weak-strong stability and phase-field approximation
of interface evolution problems in fluid mechanics and in material sciences.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587
chicago: Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation
of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.”
Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587.
ieee: A. Marveggio, “Weak-strong stability and phase-field approximation of interface
evolution problems in fluid mechanics and in material sciences,” Institute of
Science and Technology Austria, 2023.
ista: Marveggio A. 2023. Weak-strong stability and phase-field approximation of
interface evolution problems in fluid mechanics and in material sciences. Institute
of Science and Technology Austria.
mla: Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of
Interface Evolution Problems in Fluid Mechanics and in Material Sciences.
Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587.
short: A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface
Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science
and Technology Austria, 2023.
date_created: 2023-11-21T11:41:05Z
date_published: 2023-11-21T00:00:00Z
date_updated: 2023-11-30T13:25:03Z
day: '21'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
doi: 10.15479/at:ista:14587
ec_funded: 1
file:
- access_level: open_access
checksum: 6c7db4cc86da6cdc79f7f358dc7755d4
content_type: application/pdf
creator: amarvegg
date_created: 2023-11-29T09:09:31Z
date_updated: 2023-11-29T09:09:31Z
file_id: '14626'
file_name: thesis_Marveggio.pdf
file_size: 2881100
relation: main_file
success: 1
- access_level: open_access
checksum: 52f28bdf95ec82cff39f3685f9c48e7d
content_type: application/zip
creator: amarvegg
date_created: 2023-11-29T09:10:19Z
date_updated: 2023-11-29T09:28:30Z
file_id: '14627'
file_name: Thesis_Marveggio.zip
file_size: 10189696
relation: source_file
file_date_updated: 2023-11-29T09:28:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: '228'
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
- 2663 - 337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '11842'
relation: part_of_dissertation
status: public
- id: '14597'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: Weak-strong stability and phase-field approximation of interface evolution
problems in fluid mechanics and in material sciences
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '13135'
abstract:
- lang: eng
text: In this paper we consider a class of stochastic reaction-diffusion equations.
We provide local well-posedness, regularity, blow-up criteria and positivity of
solutions. The key novelties of this work are related to the use transport noise,
critical spaces and the proof of higher order regularity of solutions – even in
case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity
estimates and sharp blow-up criteria. We view the results of this paper as a general
toolbox for establishing global well-posedness for a large class of reaction-diffusion
systems of practical interest, of which many are completely open. In our follow-up
work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra
equations and the Brusselator model.
acknowledgement: The first author has received funding from the European Research
Council (ERC) under the European Union's Horizon 2020 research and innovation programme
(grant agreement No. 948819) Image 1. The second author is supported by the VICI
subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: 'Agresti A, Veraar M. Reaction-diffusion equations with transport noise and
critical superlinear diffusion: Local well-posedness and positivity. Journal
of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038'
apa: 'Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport
noise and critical superlinear diffusion: Local well-posedness and positivity.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038'
chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with
Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.'
ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Local well-posedness and positivity,” Journal
of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.'
ista: 'Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Local well-posedness and positivity. Journal
of Differential Equations. 368(9), 247–300.'
mla: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport
Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp.
247–300, doi:10.1016/j.jde.2023.05.038.'
short: A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.
date_created: 2023-06-18T22:00:45Z
date_published: 2023-09-25T00:00:00Z
date_updated: 2024-01-29T11:04:41Z
day: '25'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jde.2023.05.038
ec_funded: 1
external_id:
isi:
- '001019018700001'
file:
- access_level: open_access
checksum: 246b703b091dfe047bfc79abf0891a63
content_type: application/pdf
creator: dernst
date_created: 2024-01-29T11:03:09Z
date_updated: 2024-01-29T11:03:09Z
file_id: '14895'
file_name: 2023_JourDifferentialEquations_Agresti.pdf
file_size: 834638
relation: main_file
success: 1
file_date_updated: 2024-01-29T11:03:09Z
has_accepted_license: '1'
intvolume: ' 368'
isi: 1
issue: '9'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 247-300
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Differential Equations
publication_identifier:
eissn:
- 1090-2732
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Reaction-diffusion equations with transport noise and critical superlinear
diffusion: Local well-posedness and positivity'
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: 368
year: '2023'
...
---
_id: '12486'
abstract:
- lang: eng
text: This paper is concerned with the problem of regularization by noise of systems
of reaction–diffusion equations with mass control. It is known that strong solutions
to such systems of PDEs may blow-up in finite time. Moreover, for many systems
of practical interest, establishing whether the blow-up occurs or not is an open
question. Here we prove that a suitable multiplicative noise of transport type
has a regularizing effect. More precisely, for both a sufficiently noise intensity
and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary
large time. Global existence is shown for the case of exponentially decreasing
mass. The proofs combine and extend recent developments in regularization by noise
and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between
the two areas.
acknowledgement: "The author has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio
Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti
for her support in creating the picture. The author\r\nthanks the anonymous referee
for helpful comments. "
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
citation:
ama: 'Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems
of reaction-diffusion equations. Stochastics and Partial Differential Equations:
Analysis and Computations. 2023. doi:10.1007/s40072-023-00319-4'
apa: 'Agresti, A. (2023). Delayed blow-up and enhanced diffusion by transport noise
for systems of reaction-diffusion equations. Stochastics and Partial Differential
Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-023-00319-4'
chicago: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport
Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature, 2023.
https://doi.org/10.1007/s40072-023-00319-4.'
ieee: 'A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for
systems of reaction-diffusion equations,” Stochastics and Partial Differential
Equations: Analysis and Computations. Springer Nature, 2023.'
ista: 'Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise
for systems of reaction-diffusion equations. Stochastics and Partial Differential
Equations: Analysis and Computations.'
mla: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise
for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential
Equations: Analysis and Computations, Springer Nature, 2023, doi:10.1007/s40072-023-00319-4.'
short: 'A. Agresti, Stochastics and Partial Differential Equations: Analysis and
Computations (2023).'
date_created: 2023-02-02T10:45:47Z
date_published: 2023-11-28T00:00:00Z
date_updated: 2023-12-18T07:53:45Z
day: '28'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-023-00319-4
ec_funded: 1
external_id:
arxiv:
- '2207.08293'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s40072-023-00319-4
month: '11'
oa: 1
oa_version: Submitted Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: epub_ahead
publisher: Springer Nature
scopus_import: '1'
status: public
title: Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion
equations
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
year: '2023'
...
---
_id: '13043'
abstract:
- lang: eng
text: "We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction\r\nof a gradient flow calibration in the sense
of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends
the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting
along triple junctions."
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- 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
citation:
ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484
apa: Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature
flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023.
https://doi.org/10.4171/IFB/484.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS
Press, pp. 37–107, 2023.
ista: Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow
of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1,
EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484.
short: S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107.
date_created: 2023-05-21T22:01:06Z
date_published: 2023-04-20T00:00:00Z
date_updated: 2023-08-01T14:43:29Z
day: '20'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.4171/IFB/484
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
isi:
- '000975817300002'
file:
- access_level: open_access
checksum: 622422484810441e48f613e968c7e7a4
content_type: application/pdf
creator: dernst
date_created: 2023-05-22T07:24:13Z
date_updated: 2023-05-22T07:24:13Z
file_id: '13045'
file_name: 2023_Interfaces_Hensel.pdf
file_size: 867876
relation: main_file
success: 1
file_date_updated: 2023-05-22T07:24:13Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 37-107
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Interfaces and Free Boundaries
publication_identifier:
eissn:
- 1463-9971
issn:
- 1463-9963
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '10013'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Weak-strong uniqueness for the mean curvature flow of double bubbles
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: 25
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: '11842'
abstract:
- lang: eng
text: We consider the flow of two viscous and incompressible fluids within a bounded
domain modeled by means of a two-phase Navier–Stokes system. The two fluids are
assumed to be immiscible, meaning that they are separated by an interface. With
respect to the motion of the interface, we consider pure transport by the fluid
flow. Along the boundary of the domain, a complete slip boundary condition for
the fluid velocities and a constant ninety degree contact angle condition for
the interface are assumed. In the present work, we devise for the resulting evolution
problem a suitable weak solution concept based on the framework of varifolds and
establish as the main result a weak-strong uniqueness principle in 2D. The proof
is based on a relative entropy argument and requires a non-trivial further development
of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech.
Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects
of the necessarily singular geometry of the evolving fluid domains, we work for
simplicity in the regime of same viscosities for the two fluids.
acknowledgement: The authors warmly thank their former resp. current PhD advisor Julian
Fischer for the suggestion of this problem and for valuable initial discussions
on the subjects of this paper. This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 948819) , and from the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1
– 390685813.
article_number: '93'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation
for two fluids with ninety degree contact angle and same viscosities. Journal
of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2
apa: Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2
chicago: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same
Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature,
2022. https://doi.org/10.1007/s00021-022-00722-2.
ieee: S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities,”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature,
2022.
ista: Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. 24(3), 93.
mla: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature,
2022, doi:10.1007/s00021-022-00722-2.
short: S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).
date_created: 2022-08-14T22:01:45Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2023-11-30T13:25:02Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00021-022-00722-2
ec_funded: 1
external_id:
arxiv:
- '2112.11154'
isi:
- '000834834300001'
file:
- access_level: open_access
checksum: 75c5f286300e6f0539cf57b4dba108d5
content_type: application/pdf
creator: cchlebak
date_created: 2022-08-16T06:55:22Z
date_updated: 2022-08-16T06:55:22Z
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file_size: 2045570
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intvolume: ' 24'
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- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Mathematical Fluid Mechanics
publication_identifier:
eissn:
- 1422-6952
issn:
- 1422-6928
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '14587'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety
degree contact angle and same viscosities
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: 24
year: '2022'
...
---
_id: '12079'
abstract:
- lang: eng
text: We extend the recent rigorous convergence result of Abels and Moser (SIAM
J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning
convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin
boundary condition towards evolution by mean curvature flow with constant contact
angle. More precisely, in the present work we manage to remove the perturbative
assumption on the contact angle being close to 90∘. We establish under usual double-well
type assumptions on the potential and for a certain class of boundary energy densities
the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π).
For a very specific form of the boundary energy density, we even obtain from our
methods a sharp convergence rate of order ε; again for general contact angles
α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic
expansions and stability estimates for the linearized Allen–Cahn operator. Instead,
we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233,
2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy
technique. We develop a careful adaptation of their approach in order to encode
the constant contact angle condition. In fact, we perform this task at the level
of the notion of gradient flow calibrations. This concept was recently introduced
in the context of weak-strong uniqueness for multiphase mean curvature flow by
Fischer et al. (arXiv:2003.05478v2).
acknowledgement: "This Project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy—EXC-2047/1 - 390685813.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_number: '201'
article_processing_charge: No
article_type: original
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: 'Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary
contact energy: The non-perturbative regime. Calculus of Variations and Partial
Differential Equations. 2022;61(6). doi:10.1007/s00526-022-02307-3'
apa: 'Hensel, S., & Moser, M. (2022). Convergence rates for the Allen–Cahn equation
with boundary contact energy: The non-perturbative regime. Calculus of Variations
and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-022-02307-3'
chicago: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations. Springer Nature, 2022. https://doi.org/10.1007/s00526-022-02307-3.'
ieee: 'S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime,” Calculus of Variations
and Partial Differential Equations, vol. 61, no. 6. Springer Nature, 2022.'
ista: 'Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime. Calculus of Variations and
Partial Differential Equations. 61(6), 201.'
mla: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations, vol. 61, no. 6, 201, Springer
Nature, 2022, doi:10.1007/s00526-022-02307-3.'
short: S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations
61 (2022).
date_created: 2022-09-11T22:01:54Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2023-08-03T13:48:30Z
day: '24'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00526-022-02307-3
ec_funded: 1
external_id:
isi:
- '000844247300008'
file:
- access_level: open_access
checksum: b2da020ce50440080feedabeab5b09c4
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T08:56:01Z
date_updated: 2023-01-20T08:56:01Z
file_id: '12320'
file_name: 2022_Calculus_Hensel.pdf
file_size: 1278493
relation: main_file
success: 1
file_date_updated: 2023-01-20T08:56:01Z
has_accepted_license: '1'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates for the Allen–Cahn equation with boundary contact energy:
The non-perturbative regime'
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: 61
year: '2022'
...
---
_id: '10007'
abstract:
- lang: eng
text: The present thesis is concerned with the derivation of weak-strong uniqueness
principles for curvature driven interface evolution problems not satisfying a
comparison principle. The specific examples being treated are two-phase Navier-Stokes
flow with surface tension, modeling the evolution of two incompressible, viscous
and immiscible fluids separated by a sharp interface, and multiphase mean curvature
flow, which serves as an idealized model for the motion of grain boundaries in
an annealing polycrystalline material. Our main results - obtained in joint works
with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation
of geometric singularities due to topology changes, the weak solution concept
of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with
surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial
Differential Equations 55, 2016) to multiphase mean curvature flow (for networks
in R^2 or double bubbles in R^3) represents the unique solution to these interface
evolution problems within the class of classical solutions, respectively. To the
best of the author's knowledge, for interface evolution problems not admitting
a geometric comparison principle the derivation of a weak-strong uniqueness principle
represented an open problem, so that the works contained in the present thesis
constitute the first positive results in this direction. The key ingredient of
our approach consists of the introduction of a novel concept of relative entropies
for a class of curvature driven interface evolution problems, for which the associated
energy contains an interfacial contribution being proportional to the surface
area of the evolving (network of) interface(s). The interfacial part of the relative
entropy gives sufficient control on the interface error between a weak and a classical
solution, and its time evolution can be computed, at least in principle, for any
energy dissipating weak solution concept. A resulting stability estimate for the
relative entropy essentially entails the above mentioned weak-strong uniqueness
principles. The present thesis contains a detailed introduction to our relative
entropy approach, which in particular highlights potential applications to other
problems in curvature driven interface evolution not treated in this thesis.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: 'Hensel S. Curvature driven interface evolution: Uniqueness properties of weak
solution concepts. 2021. doi:10.15479/at:ista:10007'
apa: 'Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007'
chicago: 'Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021.
https://doi.org/10.15479/at:ista:10007.'
ieee: 'S. Hensel, “Curvature driven interface evolution: Uniqueness properties of
weak solution concepts,” Institute of Science and Technology Austria, 2021.'
ista: 'Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria.'
mla: 'Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts. Institute of Science and Technology Austria, 2021,
doi:10.15479/at:ista:10007.'
short: 'S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of
Weak Solution Concepts, Institute of Science and Technology Austria, 2021.'
date_created: 2021-09-13T11:12:34Z
date_published: 2021-09-14T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '14'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
doi: 10.15479/at:ista:10007
ec_funded: 1
file:
- access_level: closed
checksum: c8475faaf0b680b4971f638f1db16347
content_type: application/x-zip-compressed
creator: shensel
date_created: 2021-09-13T11:03:24Z
date_updated: 2021-09-15T14:37:30Z
file_id: '10008'
file_name: thesis_final_Hensel.zip
file_size: 15022154
relation: source_file
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checksum: 1a609937aa5275452822f45f2da17f07
content_type: application/pdf
creator: shensel
date_created: 2021-09-13T14:18:56Z
date_updated: 2021-09-14T09:52:47Z
file_id: '10014'
file_name: thesis_final_Hensel.pdf
file_size: 6583638
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file_date_updated: 2021-09-15T14:37:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '300'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10012'
relation: part_of_dissertation
status: public
- id: '10013'
relation: part_of_dissertation
status: public
- id: '7489'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: 'Curvature driven interface evolution: Uniqueness properties of weak solution
concepts'
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10011'
abstract:
- lang: eng
text: We propose a new weak solution concept for (two-phase) mean curvature flow
which enjoys both (unconditional) existence and (weak-strong) uniqueness properties.
These solutions are evolving varifolds, just as in Brakke's formulation, but are
coupled to the phase volumes by a simple transport equation. First, we show that,
in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461,
(1993)], any limit point of solutions to the Allen-Cahn equation is a varifold
solution in our sense. Second, we prove that any calibrated flow in the sense
of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean
curvature flow - is unique in the class of our new varifold solutions. This is
in sharp contrast to the case of Brakke flows, which a priori may disappear at
any given time and are therefore fatally non-unique. Finally, we propose an extension
of the solution concept to the multi-phase case which is at least guaranteed to
satisfy a weak-strong uniqueness principle.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
The content of this paper was developed and parts of it were written during a visit
of the first author to the Hausdorff Center of Mathematics (HCM), University of
Bonn. The hospitality and the support of HCM are gratefully acknowledged.
article_number: '2109.04233'
article_processing_charge: No
arxiv: 1
author:
- 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
citation:
ama: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow:
Convergence of the Allen-Cahn equation and weak-strong uniqueness. arXiv.
doi:10.48550/arXiv.2109.04233'
apa: 'Hensel, S., & Laux, T. (n.d.). A new varifold solution concept for mean
curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness.
arXiv. https://doi.org/10.48550/arXiv.2109.04233'
chicago: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for
Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2109.04233.'
ieee: 'S. Hensel and T. Laux, “A new varifold solution concept for mean curvature
flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,” arXiv.
.'
ista: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow:
Convergence of the Allen-Cahn equation and weak-strong uniqueness. arXiv, 2109.04233.'
mla: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean
Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.”
ArXiv, 2109.04233, doi:10.48550/arXiv.2109.04233.'
short: S. Hensel, T. Laux, ArXiv (n.d.).
date_created: 2021-09-13T12:17:10Z
date_published: 2021-09-09T00:00:00Z
date_updated: 2023-05-03T10:34:38Z
day: '09'
department:
- _id: JuFi
doi: 10.48550/arXiv.2109.04233
ec_funded: 1
external_id:
arxiv:
- '2109.04233'
keyword:
- Mean curvature flow
- gradient flows
- varifolds
- weak solutions
- weak-strong uniqueness
- calibrated geometry
- gradient-flow calibrations
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2109.04233
month: '09'
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
status: public
title: 'A new varifold solution concept for mean curvature flow: Convergence of the
Allen-Cahn equation and weak-strong uniqueness'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '10013'
abstract:
- lang: eng
text: We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction of a gradient-flow calibration in the sense
of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster.
This extends the two-dimensional construction to the three-dimensional case of
surfaces meeting along triple junctions.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
article_number: '2108.01733'
article_processing_charge: No
arxiv: 1
author:
- 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
citation:
ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv. doi:10.48550/arXiv.2108.01733
apa: Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature
flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” arXiv. .
ista: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv, 2108.01733.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733.
short: S. Hensel, T. Laux, ArXiv (n.d.).
date_created: 2021-09-13T12:17:11Z
date_published: 2021-08-03T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '03'
department:
- _id: JuFi
doi: 10.48550/arXiv.2108.01733
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2108.01733
month: '08'
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: '13043'
relation: later_version
status: public
- id: '10007'
relation: dissertation_contains
status: public
status: public
title: Weak-strong uniqueness for the mean curvature flow of double bubbles
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...