Multi-marginal Monge-Kantorovich transport problems: A characterization of solutions

Abstract: We shall present a measure theoretical approach for which together with the Kantorovich duality provide an efficient tool to study the optimal transport problem. Specifically, we study the support of optimal plans where the cost function does not satisfy the classical twist condition in the two marginal problem as well as in the multi-marginal case when twistedness is limited to certain subsets.