Limits of density-constrained optimal transport

We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of Γ -convergence for two singular phenomena. First, for densities constrained near a hyperplane we recover the optimal flow through an infinitesimal permeable membrane. Second, for...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2022-04, Vol.61 (2), Article 70
Main Authors: Gladbach, Peter, Kopfer, Eva
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Constraints
Control
Density
Hyperplanes
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Porous media
Systems Theory
Theoretical
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Summary:We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of Γ -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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-02163-7