The obstacle problem for Monge-Ampère type equations in non-convex domains

Jingang Xiong; Jiguang Bao

doi:10.3934/cpaa.2011.10.59

Article Contents

2011, Volume 10, Issue 1: 59-68. Doi: 10.3934/cpaa.2011.10.59

This issue Previous Article The existence of weak solutions for a generalized Camassa-Holm equation Next Article A comparison principle for a Sobolev gradient semi-flow

The obstacle problem for Monge-Ampère type equations in non-convex domains

Jingang Xiong^1, and
Jiguang Bao^2,

1.
School of Mathematical Sciences, Beijing Normal University
2.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875

Received: December 2009

Revised: March 2010

Published: January 2011

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Abstract

In this paper, we consider the obstacle problem for Monge-Ampère type equations which include prescribed Gauss curvature equation as a special case. We establish $C^{1,1}$ regularity of the greatest viscosity solution in non-convex domains.

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Mathematics Subject Classification: Primary: 35J60; Secondary: 35R35.

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