[{"_id":"12959","date_updated":"2023-10-04T11:34:49Z","type":"journal_article","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00526-023-02472-z","publisher":"Springer Nature","quality_controlled":"1","ddc":["510"],"isi":1,"year":"2023","external_id":{"isi":["000980588900001"],"arxiv":["2110.15321"]},"ec_funded":1,"acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF).","date_published":"2023-04-28T00:00:00Z","status":"public","publication":"Calculus of Variations and Partial Differential Equations","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"volume":62,"date_created":"2023-05-14T22:01:00Z","article_type":"original","day":"28","scopus_import":"1","author":[{"full_name":"Gladbach, Peter","last_name":"Gladbach","first_name":"Peter"},{"first_name":"Eva","full_name":"Kopfer, Eva","last_name":"Kopfer"},{"first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas"},{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","last_name":"Portinale"}],"title":"Homogenisation of dynamical optimal transport on periodic graphs","oa_version":"Published Version","file_date_updated":"2023-10-04T11:34:10Z","publication_identifier":{"eissn":["1432-0835"],"issn":["0944-2669"]},"publication_status":"published","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"        62","abstract":[{"text":"This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs.","lang":"eng"}],"department":[{"_id":"JaMa"}],"article_number":"143","file":[{"creator":"dernst","date_updated":"2023-10-04T11:34:10Z","date_created":"2023-10-04T11:34:10Z","file_size":1240995,"file_id":"14393","access_level":"open_access","content_type":"application/pdf","success":1,"file_name":"2023_CalculusEquations_Gladbach.pdf","checksum":"359bee38d94b7e0aa73925063cb8884d","relation":"main_file"}],"arxiv":1,"month":"04","citation":{"ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. 2023;62(5). doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023).","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5. Springer Nature, 2023.","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>.","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143.","mla":"Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5, 143, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>.","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>"},"issue":"5","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality."}],"intvolume":"        54","publication_status":"published","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"author":[{"first_name":"Dominik L","full_name":"Forkert, Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","last_name":"Forkert"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","last_name":"Maas","first_name":"Jan","orcid":"0000-0002-0845-1338"},{"last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"day":"18","scopus_import":"1","oa_version":"Preprint","title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","volume":54,"article_type":"original","date_created":"2022-08-07T22:01:59Z","oa":1,"language":[{"iso":"eng"}],"issue":"4","citation":{"ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022.","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(4):4297-4333. doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>","apa":"Forkert, D. L., Maas, J., &#38; Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>.","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>.","ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"month":"07","department":[{"_id":"JaMa"}],"page":"4297-4333","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2008.10962","open_access":"1"}],"quality_controlled":"1","doi":"10.1137/21M1410968","article_processing_charge":"No","publisher":"Society for Industrial and Applied Mathematics","date_updated":"2023-08-03T12:37:21Z","_id":"11739","type":"journal_article","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"SIAM Journal on Mathematical Analysis","ec_funded":1,"acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","date_published":"2022-07-18T00:00:00Z","isi":1,"year":"2022","external_id":{"arxiv":["2008.10962"],"isi":["000889274600001"]},"related_material":{"record":[{"id":"10022","status":"public","relation":"earlier_version"}]},"keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"]},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Portinale, Lorenzo. <i>Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>.","apa":"Portinale, L. (2021). <i>Discrete-to-continuum limits of transport problems and gradient flows in the space of measures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria.","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>.","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021.","ama":"Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>"},"language":[{"iso":"eng"}],"oa":1,"file":[{"relation":"source_file","checksum":"8cd60dcb8762e8f21867e21e8001e183","file_name":"tex_and_pictures.zip","access_level":"closed","content_type":"application/x-zip-compressed","file_id":"10032","date_created":"2021-09-21T09:17:34Z","file_size":3876668,"date_updated":"2022-03-10T12:14:42Z","creator":"cchlebak"},{"checksum":"9789e9d967c853c1503ec7f307170279","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"thesis_portinale_Final (1).pdf","file_id":"10047","date_updated":"2021-09-27T11:14:31Z","creator":"cchlebak","date_created":"2021-09-27T11:14:31Z","file_size":2532673}],"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"month":"09","supervisor":[{"first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","last_name":"Maas"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","file_date_updated":"2022-03-10T12:14:42Z","abstract":[{"text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"has_accepted_license":"1","date_created":"2021-09-21T09:14:15Z","title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","oa_version":"Published Version","author":[{"last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"day":"22","date_published":"2021-09-22T00:00:00Z","acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","project":[{"_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"status":"public","degree_awarded":"PhD","related_material":{"record":[{"id":"10022","relation":"part_of_dissertation","status":"public"},{"id":"9792","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"7573"}]},"year":"2021","ddc":["515"],"type":"dissertation","date_updated":"2023-09-07T13:31:06Z","_id":"10030","publisher":"Institute of Science and Technology Austria","doi":"10.15479/at:ista:10030","article_processing_charge":"No","alternative_title":["ISTA Thesis"]},{"oa":1,"language":[{"iso":"eng"}],"issue":"11","citation":{"ista":"Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212.","chicago":"Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>.","apa":"Abbatiello, A., Bulíček, M., &#38; Maringová, E. (2021). On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>","mla":"Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>.","ama":"Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(11):2165-2212. doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>","ieee":"A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary condition for Navier-Stokes-like problems,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212, 2021.","short":"A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"month":"10","department":[{"_id":"JuFi"}],"file":[{"checksum":"8c0a9396335f0b70e1f5cbfe450a987a","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_name":"2021_MathModelsMethods_Abbatiello.pdf","success":1,"file_id":"11385","date_updated":"2022-05-16T10:55:45Z","creator":"dernst","file_size":795483,"date_created":"2022-05-16T10:55:45Z"}],"has_accepted_license":"1","tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)"},"abstract":[{"lang":"eng","text":"The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting."}],"intvolume":"        31","publication_status":"published","publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"file_date_updated":"2022-05-16T10:55:45Z","author":[{"last_name":"Abbatiello","full_name":"Abbatiello, Anna","first_name":"Anna"},{"full_name":"Bulíček, Miroslav","last_name":"Bulíček","first_name":"Miroslav"},{"first_name":"Erika","last_name":"Maringová","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","full_name":"Maringová, Erika"}],"scopus_import":"1","day":"13","title":"On the dynamic slip boundary condition for Navier-Stokes-like problems","oa_version":"Published Version","volume":31,"article_type":"original","date_created":"2021-12-26T23:01:27Z","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF"}],"publication":"Mathematical Models and Methods in Applied Sciences","status":"public","date_published":"2021-10-13T00:00:00Z","acknowledgement":"The research of A. Abbatiello is supported by Einstein Foundation, Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No. 20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian Science Fund (FWF), grants P30000, W1245, and F65.","year":"2021","isi":1,"external_id":{"arxiv":["2009.09057"],"isi":["000722309400001"]},"page":"2165-2212","ddc":["510"],"quality_controlled":"1","doi":"10.1142/S0218202521500470","article_processing_charge":"No","publisher":"World Scientific Publishing","date_updated":"2023-08-17T06:29:01Z","_id":"10575","type":"journal_article"},{"status":"public","publication":"Journal de Mathematiques Pures et Appliquees","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"call_identifier":"FWF","grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"date_published":"2020-07-01T00:00:00Z","acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"10030"}]},"external_id":{"isi":["000539439400008"],"arxiv":["1905.05757"]},"year":"2020","isi":1,"page":"204-234","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1905.05757"}],"publisher":"Elsevier","article_processing_charge":"No","doi":"10.1016/j.matpur.2020.02.008","type":"journal_article","_id":"7573","date_updated":"2023-09-07T13:31:05Z","language":[{"iso":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">https://doi.org/10.1016/j.matpur.2020.02.008</a>.","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7), 204–234.","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2020). Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">https://doi.org/10.1016/j.matpur.2020.02.008</a>","mla":"Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7, Elsevier, 2020, pp. 204–34, doi:<a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">10.1016/j.matpur.2020.02.008</a>.","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. 2020;139(7):204-234. doi:<a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">10.1016/j.matpur.2020.02.008</a>","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7. Elsevier, pp. 204–234, 2020.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234."},"issue":"7","month":"07","arxiv":1,"department":[{"_id":"JaMa"}],"abstract":[{"lang":"eng","text":"This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport."}],"intvolume":"       139","publication_identifier":{"issn":["00217824"]},"publication_status":"published","title":"Homogenisation of one-dimensional discrete optimal transport","oa_version":"Preprint","day":"01","scopus_import":"1","author":[{"first_name":"Peter","full_name":"Gladbach, Peter","last_name":"Gladbach"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan"},{"last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"date_created":"2020-03-08T23:00:47Z","article_type":"original","volume":139}]