Calculus of Variations and Geometric Measure Theory
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T. Champion - L. De Pascale

The Monge problem for strictly convex norms in $R^d$

created by depascal on 07 May 2008
modified on 22 Sep 2010


Published Paper

Inserted: 7 may 2008
Last Updated: 22 sep 2010

Journal: Journ. of the Eur. Math. Soc.
Volume: 12
Number: 6
Pages: 1355-1369
Year: 2010

The published version is available at: http:/www.ems-ph.orgjournalsshowissue.php?issn=1435-9855&vol=12&iss=6


We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of $\R^d$ under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.

Keywords: Monge-Kantorovich problem, optimal transport problem, cyclical monotonicity


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