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arXiv · 1608.08780

Continuity and estimates for multimarginal optimal transportation problems with singular costs

Giuseppe Buttazzo·Thierry Champion·Luigi De Pascale
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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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Giuseppe Buttazzo, Thierry Champion, Luigi De Pascale. 2016-08-31. Continuity and estimates for multimarginal optimal transportation problems with singular costs. https://arxiv.org/abs/1608.08780

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