Regularity properties of monotone measure-preserving maps

被引：1

作者：

Figalli, Alessio ^{[1
]}

Jhaveri, Yash ^{[2
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Rutgers Univ Newark, Dept Math & Comp Sci, Smith Hall,101 Warren St, Newark, NJ 07102 USA

来源：

ADVANCED NONLINEAR STUDIES | 2023年 / 23卷 / 01期

基金：

欧洲研究理事会;

关键词：

optimal transport maps; Monge-Ampere equation; doubling measures; unbounded support;

D O I：

10.1515/ans-2022-0057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex domain and, on the low-regularity end, between domains carrying certain invariant measures.

引用

页数：11

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