Uniqueness and Monge solutions in the multi-marginal optimal transportation problem

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

We study a multi-marginal optimal transportation problem. Under certain
conditions on the cost function and the first marginal, we prove that the
solution to the relaxed, Kantorovich version of the problem induces a solution
to the Monge problem and that the solutions to both problems are unique.

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