Liouville theorem for the nonlinear Poisson equation on manifolds

被引：3

作者：

Ma, Li ^{[1
]}

Witt, Ingo ^{[2
]}

机构：

[1] Henan Normal Univ, Dept Math, Xinxiang 453007, Peoples R China

[2] Univ Gottingen, Math Inst, D-37073 Gottingen, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 416卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Liouville theorem; Modica type gradient estimate; Nonlinear Poisson equation;

D O I：

10.1016/j.jmaa.2014.03.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we study a Modica type gradient estimate for smooth solutions to general non-linear Poisson equation Delta(u) - f(u) = 0, in M-n, u : M-n -> R where (M, g) is a complete Riemannian manifold with bounded geometry and non-negative Ricci curvature and f is the derivative of the non-negative smooth function F(u) on R. Then we use this gradient estimate to conclude a Lionville theorem. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：800 / 804

页数：5

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