The Monge problem for strictly convex norms in
Thierry Champion
Université de Toulon et du Var, La Garde, FranceLuigi De Pascale
Università di Pisa, Italy
![The Monge problem for strictly convex norms in $\mathbb{R}^d$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-12-issue-6.png&w=3840&q=90)
Abstract
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 . J. Eur. Math. Soc. 12 (2010), no. 6, pp. 1355–1369
DOI 10.4171/JEMS/234