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

2010/07/02 by Brendan Pass, Pass, Brendan
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.1007.0424

openalex publication_date 2010/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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