一类加权非线性椭圆方程的梯度估计和liouville型定理。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-10 DOI:10.1186/s13660-018-1705-z

Bingqing Ma, Yongli Dong

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引用次数: 3

摘要

我们考虑光滑度量度量空间上以下非线性椭圆方程的正解的梯度估计[公式:见文]:[公式:见文]，其中a, b是两个实常数。当∞-Bakry-Émery Ricci曲率从下有界时，我们得到一个不依赖于[公式:见文]的全局梯度估计。特别地，我们发现在一些适当的假设下，上述方程的任何有界正解都必须是常数。

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Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation.

We consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a smooth metric measure space [Formula: see text]: [Formula: see text] where a, b are two real constants. When the ∞-Bakry-Émery Ricci curvature is bounded from below, we obtain a global gradient estimate which is not dependent on [Formula: see text]. In particular, we find that any bounded positive solution of the above equation must be constant under some suitable assumptions.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.