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
收藏
页码：1355 / 1369
页数：15
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