Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces

In this paper we extend the duality theory of the multi-marginal optimal transport problem for cost functions depending on a decreasing function of the distance (not necessarily bounded). This class of cost functions appears in the context of SCE Density Functional Theory introduced in Strong-interaction limit of density-functional theory by Seidl [Phys. Rev. A 60 (1999) 4387].

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