  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.

Optimization and Control