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arXiv · 1903.12104

Limits of density-constrained optimal transport

Peter Gladbach·Eva Kopfer
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Abstract

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.

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Peter Gladbach, Eva Kopfer. 2019-03-28. Limits of density-constrained optimal transport. https://arxiv.org/abs/1903.12104

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