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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). \udThis 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