article published yes Peter Gladbach author Eva Kopfer author Jan Maas author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338 Lorenzo Portinale author 30AD2CBC-F248-11E8-B48F-1D18A9856A87 JaMa department Optimal Transport and Stochastic Dynamics project Taming Complexity in Partial Differential Systems project Dissipation and dispersion in nonlinear partial differential equations project This paper deals with the large-scale behaviour of dynamical optimal transport on Zd -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 -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. https://research-explorer.ista.ac.at/download/12959/14393/2023_CalculusEquations_Gladbach.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer Nature2023 eng 0944-2669 1432-0835 2110.15321 37131846 00098058890000110.1007/s00526-023-02472-z 625 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> 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>. 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> 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. 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>. 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. P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023). 129592023-05-14T22:01:00Z2025-05-15T10:54:12Z