An exterior optimal transport problem - Centre de mathématiques appliquées (CMAP)
Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2024

An exterior optimal transport problem

Un problème de transport optimal extérieur

Résumé

This paper deals with a variant of the optimal transportation problem. Given f ∈ L 1 (R d , [0, 1]) and a cost function c ∈ C(R d × R d) of the form c(x, y) = k(y − x), we minimise ∫ c dγ among transport plans γ whose first marginal is f and whose second marginal is not prescribed but constrained to be smaller than 1 − f. Denoting by Υ(f) the infimum of this problem, we then consider the maximisation problem sup{Υ(f) : ∫ f = m} where m > 0 is given. We prove that maximisers exist under general assumptions on k, and that for k radial, increasing and coercive these maximisers are the characteristic functions of the balls of volume m.
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Dates et versions

hal-04196005 , version 1 (05-09-2023)
hal-04196005 , version 2 (08-10-2024)

Identifiants

Citer

Jules Candau-Tilh, Michael Goldman, Benoît Merlet. An exterior optimal transport problem. Calculus of Variations and Partial Differential Equations, inPress. ⟨hal-04196005v2⟩
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