The Monge problem for strictly convex norms in Rd

被引：26

作者：

Champion, Thierry ^{[1
]}

De Pascale, Luigi ^{[2
]}

机构：

[1] Univ Sud Toulon Var, UFR Sci & Tech, Inst Math Toulon & Var, F-83957 La Garde, France

[2] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2010年 / 12卷 / 06期

关键词：

Monge-Kantorovich problem; optimal transport problem; cyclical monotonicity; TRANSPORT DENSITY; OPTIMALITY; EXISTENCE;

D O I：

10.4171/JEMS/234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1355 / 1369

页数：15

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