A LIOUVILLE THEOREM FOR SOLUTIONS TO THE LINEARIZED MONGE-AMPERE EQUATION

被引：7

作者：

Savin, Ovidiu ^{[1
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 03期

基金：

美国国家科学基金会;

关键词：

Monge-Ampere equation; Harnack inequality; PARTIAL-DIFFERENTIAL-EQUATIONS;

D O I：

10.3934/dcds.2010.28.865

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that global Lipschitz solutions to the linearized Monge-Ampere equation L(phi)u := Sigma phi(ij) u(ij) = 0 must be linear in 2D. The function phi is assumed to have the Monge-Ampere measure det D(2)phi bounded away from 0 and infinity.

引用

页码：865 / 873

页数：9

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