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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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https://hal-univ-tln.archives-ouvertes.fr/hal-01358148
Contributor : Thierry Champion <>
Submitted on : Wednesday, August 31, 2016 - 10:55:01 AM
Last modification on : Friday, April 24, 2020 - 2:16:08 PM
Document(s) archivé(s) le : Friday, December 2, 2016 - 8:50:03 AM

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  • HAL Id : hal-01358148, version 1
  • ARXIV : 1608.08780

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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, Springer Verlag (Germany), 2018. ⟨hal-01358148⟩

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