Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs

Giuseppe Buttazzo (1) , Thierry Champion (2) , Luigi de Pascale (1, 3)

1 Dipartimento di Matematica [Pisa]
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 DiMal - Dipartimento di Matematica e Informatica [Firenze]

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.

Domains: Optimization and Control [math.OC]

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⟩