ON THE REGULARITY OF THE COMPLEX MONGE-AMPERE EQUATIONS

被引：7

作者：

He, Weiyong ^{[1
]}

机构：

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 05期

关键词：

The complex Mange-Ampere equation; regularity; DIRICHLET PROBLEM; VARIATIONAL PROPERTIES;

D O I：

10.1090/S0002-9939-2011-11178-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We shall consider the regularity of solutions for the complex Monge-Ampere equations in C-n or a bounded domain. First we prove interior C-2 estimates of solutions in a bounded domain for the complex Monge-Ampere equations with the assumption of an L-P bound for Delta u, p > n(2), and of a Lipschitz condition on the right-hand side. Then we shall construct a family of Pogorelov-type examples for the complex Monge-Ampere equations. These examples give generalized entire solutions (as well as viscosity solutions) of the complex Monge-Ampere equation det(u(i (j) over bar)) = 1 in C-n.

引用

页码：1719 / 1727

页数：9

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