Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs

被引：17
作者：
Buttazzo, Giuseppe [1 ]
Champion, Thierry [2 ]
De Pascale, Luigi [3 ]
机构：
[1] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, I-56127 Pisa, Italy
[2] Univ Toulon & Var, Lab IMATH, CS 60584, F-83041 Toulon 9, France
[3] Univ Firenze, Dipartimento Matemat & Informat, Viale Morgagni 67-A, I-50134 Florence, Italy
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2018年 / 78卷 / 01期
关键词：
Multimarginal optimal transportation; Monge-Kantorovich problem; Duality theory; Coulomb cost;
D O I：
10.1007/s00245-017-9403-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider some repulsive multimarginal optimal transportation problems which include, as a particular case, the Coulomb cost. We prove a regularity property of the minimizers (optimal transportation plan) from which we deduce existence and some basic regularity of a maximizer for the dual problem (Kantorovich potential). This is then applied to obtain some estimates of the cost and to the study of continuity properties.
引用
收藏
页码：185 / 200
页数：16
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