The Monge problem for strictly convex norms in $\mathbb{R}^d$

Thierry Champion; Luigi De Pascale

doi:10.4171/jems/234

JournalsjemsVol. 12, No. 6pp. 1355–1369

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

Thierry Champion
Université de Toulon et du Var, La Garde, France
Luigi De Pascale
Università di Pisa, Italy

$The Monge problem for strictly convex norms in $\mathbb{R}^d$ cover$

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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 $R^{d}$ . J. Eur. Math. Soc. 12 (2010), no. 6, pp. 1355–1369

DOI 10.4171/JEMS/234