On Pogorelov estimates for Monge-Ampère type equations

Trudinger, Neil; Liu, Jiakun

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On Pogorelov estimates for Monge-Ampère type equations

Date

2010

Authors

Trudinger, Neil

Liu, Jiakun

Publisher

American Mathematical Society

Abstract

In this paper, we prove interior second derivative estimates of Pogorelov type for a general form of Monge-Ampère equation which includes the optimal transportation equation. The estimate extends that in a previous work with Xu-Jia Wang and assumes only that the matrix function in the equation is regular with respect to the gradient variables, that is it satisfies a weak form of the condition introduced previously by Ma, Trudinger and Wang for regularity of optimal transport mappings. We also indicate briefly an application to optimal transportation.