# Limits of density-constrained optimal transport

@article{Gladbach2019LimitsOD, title={Limits of density-constrained optimal transport}, author={Peter Gladbach and Eva Kopfer}, journal={arXiv: Analysis of PDEs}, year={2019} }

We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of $\Gamma$-convergence for two singular phenomena. First, for densities constrained near a hyperplane we recover the optimal flow through an infinitesimal permeable membrane. Second, for rapidly oscillating periodic constraints we obtain the optimal flow through a homogenized porous medium.

#### One Citation

Homogenisation of dynamical optimal transport on periodic graphs

- Computer Science, Mathematics
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A homogenisation result is derived from a Γ-convergence result for action functionals on curves of measures that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. Expand

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