Augusto Gerolin, Anna Kausamo, Tapio Rajala
Published 2019-07-18Version 1
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the $\Gamma$-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.
Comments: 20 pages, 1 figure
Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost
A general condition for Monge solutions in the multi-marginal optimal transport problem
Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces
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