Optimal transportation for a quadratic cost with convex constraints and applications

Abstract

We prove existence of an optimal transport map in the MongeKantorovich problem associated to a cost c(x, y) which is not finite everywhere, but coincides with |x− y|2 if the displacement y − x belongs to a given convex set C and it is +∞ otherwise. The result is proven for C satisfying some technical assumptions allowing any convex body in R2 and any convex… (More)

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Cite this paper

@inproceedings{Jimenez2017OptimalTF, title={Optimal transportation for a quadratic cost with convex constraints and applications}, author={C. Jimenez and Filippo Santambrogio}, year={2017} }