JournalsjemsVol. 12 , No. 6DOI 10.4171/jems/234

The Monge problem for strictly convex norms in ℝ<sup><em>d</em></sup>

  • 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 ℝ<sup><em>d</em></sup> cover

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.