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.
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页码：865 / 873
页数：9
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