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.
Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs / Buttazzo, Giuseppe; Champion, Thierry; De Pascale, Luigi. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 78:(2018), pp. 185-200. [10.1007/s00245-017-9403-7]
Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs
De Pascale, Luigi
2018
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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