Inserted: 23 aug 2016
Last Updated: 23 aug 2016
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.
Keywords: duality theory, Monge-Kantorovich problem, Multimarginal optimal transportation, Coulomb cost