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.
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页码：800 / 804
页数：5
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