Interior C2,α Regularity for Potential Functions in Optimal Transportation

被引：47

作者：

Liu, Jiakun ^{[1
]}

Trudinger, Neil S. ^{[1
]}

Wang, Xu-Jia ^{[1
]}

机构：

[1] Australian Natl Univ, Ctr Math & Applicat, Canberra, ACT 0200, Australia

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2010年 / 35卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

Monge-Ampere equations; Optimal transportation; Second derivative estimates; MONGE-AMPERE EQUATION;

D O I：

10.1080/03605300903236609

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the continuity of second derivatives of solutions to the Monge-Ampere equation arising in optimal transportation. We obtain Holder and more general continuity estimates for second derivatives, when the inhomogeneous term is Holder and Dini continuous, together with corresponding regularity results for potentials.

引用

页码：165 / 184

页数：20

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