We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of Rd 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.
The Monge problem for strictly convex norms in R^N / CHAMPION T; DE PASCALE L. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 12:6(2010), pp. 1355-1369. [10.4171/JEMS/234]
The Monge problem for strictly convex norms in R^N
DE PASCALE, LUIGI
2010
Abstract
We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of Rd 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.
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