On Pogorelov estimates in optimal transportation and geometric optics

被引：31

作者：

Jiang, Feida ^{[1
]}

Trudinger, Neil S. ^{[1
]}

机构：

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

来源：

BULLETIN OF MATHEMATICAL SCIENCES | 2014年 / 4卷 / 03期

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

Monge-Ampere equations; Optimal transportation; Geometric optics; Second derivative estimates; POTENTIAL FUNCTIONS; REGULARITY; EQUATIONS;

D O I：

10.1007/s13373-014-0055-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove global and interior second derivative estimates of Pogorelov type for certain Monge-Ampere type equations, arising in optimal transportation and geometric optics, under sharp hypotheses. Specifically, for the case of generated prescribed Jacobian equations, as developed recently by the second author, we remove barrier or subsolution hypotheses assumed in previous work by Trudinger and Wang (Arch Ration Mech Anal 192:403-418, 2009), Liu and Trudinger (Discret Contin Dyn Syst Ser A 28:1121-1363, 2010), Jiang et al. (Calc Var Partial Differ Equ 49:1223-1236, 2014), resulting in new applications to optimal transportation and near field geometric optics.

引用

页码：407 / 431

页数：25

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