Inserted: 7 may 2008
Last Updated: 22 sep 2010
Journal: Journ. of the Eur. Math. Soc.
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