Uniqueness and Monge solutions in the multi-marginal optimal transportation problem
Analysis of PDEs
2010-08-27 v2
Abstract
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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Cite
@article{arxiv.1007.0424,
title = {Uniqueness and Monge solutions in the multi-marginal optimal transportation problem},
author = {Brendan Pass},
journal= {arXiv preprint arXiv:1007.0424},
year = {2010}
}
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