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Journal Articles Applied Mathematics and Optimization Year : 2018

Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs

Abstract

We consider some repulsive multimarginal optimal transportation problems which include, as a particular case, the Coulomb cost. We prove a regularity property of the minimizers (optimal transportation plan) from which we deduce existence and some basic regularity of a maximizer for the dual problem (Kantorovich potential). This is then applied to obtain some estimates of the cost and to the study of continuity properties.
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Dates and versions

hal-01358148 , version 1 (31-08-2016)

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Giuseppe Buttazzo, Thierry Champion, Luigi de Pascale. Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs. Applied Mathematics and Optimization, 2018. ⟨hal-01358148⟩
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