A localization theorem and boundary regularity for a class of degenerate Monge-Ampere equations

被引：28
作者：
Savin, Ovidiu [1 ]
机构：
[1] Columbia Univ, New York, NY 10027 USA
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 256卷 / 02期
关键词：
DIRICHLET PROBLEM;
D O I：
10.1016/j.jde.2013.08.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider degenerate Monge Ampere equations of the type det D(2)u = f in Omega, f similar to d(partial derivative Omega)(alpha) near partial derivative Omega, where d(partial derivative Omega) represents the distance to the boundary of the domain Omega and alpha > 0 is a positive power. We obtain C-2 estimates at the boundary under natural conditions on the boundary data and the right-hand side. Similar estimates in two dimensions were obtained by J.X. Hong, G. Huang and W. Wang in [3]. (C) 2013 Elsevier Inc. All rights reserved.
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收藏
页码：327 / 388
页数：62
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