Accepted Paper
Inserted: 5 jun 2009
Last Updated: 27 jul 2010
Journal: Duke Mathematical Journal
Year: 2009
Abstract:
We consider the Monge problem in a convex bounded subset of $\mathbb{R}^d$. The cost is given by a general norm, and we prove the existence of an optimal transport map under the classical assumption that the first marginal is absolutely continuous with respect to the Lebesgue measure. The approach we propose to solve this problem does not use the disintegration of measures.
Version revised on the October 16 2009 according to a first referee report.
Keywords: Monge-Kantorovich problem, optimal transport problem, cyclical monotonicity
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