An ε-regularity result for optimal transport maps between continuous densities

被引：3

作者：

Goldman, Michael ^{[1
]}

机构：

[1] Univ Paris, Lab Jacques Louis Lions LJLL, CNRS, Sorbonne Univ, 8 Pl Aurelie Nemours, F-75205 Paris 13, France

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2020年 / 31卷 / 04期

关键词：

Monge-Ampe`re equation; partial regularity; optimal transport;

D O I：

10.4171/RLM/922

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.

引用

页码：971 / 979

页数：9

共 9 条

[1] [Anonymous], 1987, ELLIPTIC DIFFERENTIA
[2] [Anonymous], 2012, APPUNTI SCUOLA NORMA
[3] PARTIAL REGULARITY FOR OPTIMAL TRANSPORT MAPS
De Philippis, Guido
Figalli, Alessio
[J]. PUBLICATIONS MATHEMATIQUES DE L IHES, 2015, (121): : 81 - 112
[4] PARTIAL REGULARITY OF BRENIER SOLUTIONS OF THE MONGE-AMPERE EQUATION
Figalli, Alessio
Kim, Young-Heon
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (02) : 559 - 565
[5] Otto Goldman F., ANN ENS
[6] Otto Goldman Huesmann F., 2019, ARXIV190509678
[7] Otto Miura F., 2020, ARXIV200208668
[8] Ried Prodhomme T., 2020, ARXIV200711549
[9] Villani C., 2003, TOPICS OPTIMAL TRANS, V58

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