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.
Cite this article
Thierry Champion, Luigi De Pascale, The Monge problem for strictly convex norms in ℝ<sup><em>d</em></sup>. J. Eur. Math. Soc. 12 (2010), no. 6, pp. 1355–1369DOI 10.4171/JEMS/234