---
_id: '12959'
abstract:
- lang: eng
  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."
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).
article_number: '143'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Peter
  full_name: Gladbach, Peter
  last_name: Gladbach
- first_name: Eva
  full_name: Kopfer, Eva
  last_name: Kopfer
- first_name: Jan
  full_name: Maas, Jan
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
- first_name: Lorenzo
  full_name: Portinale, Lorenzo
  id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
  last_name: Portinale
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>
  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>
  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>.
  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.
  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>.
  short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and
    Partial Differential Equations 62 (2023).
corr_author: '1'
date_created: 2023-05-14T22:01:00Z
date_published: 2023-04-28T00:00:00Z
date_updated: 2025-05-15T10:54:12Z
day: '28'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-023-02472-z
ec_funded: 1
external_id:
  arxiv:
  - '2110.15321'
  isi:
  - '000980588900001'
  pmid:
  - '37131846'
file:
- access_level: open_access
  checksum: 359bee38d94b7e0aa73925063cb8884d
  content_type: application/pdf
  creator: dernst
  date_created: 2023-10-04T11:34:10Z
  date_updated: 2023-10-04T11:34:10Z
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file_date_updated: 2023-10-04T11:34:10Z
fulldoi: https://doi.org/10.1007/s00526-023-02472-z
has_accepted_license: '1'
intvolume: '        62'
isi: 1
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
pmid: 1
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
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: W1245
  name: Dissipation and dispersion in nonlinear partial differential equations
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: Homogenisation of dynamical optimal transport on periodic graphs
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: 62
year: '2023'
...