Liouville theorems and Harnack inequality for a class of semilinear elliptic equations

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-01-24 DOI:10.1016/j.jde.2025.01.068

Zhihao Lu

引用次数: 0

Abstract

We give logarithmic gradient estimate and Harnack inequality for a class of semilinear elliptic equations on Riemannian manifolds with (Bakry-Émery) Ricci curvature bounded below. The nonlinear item does not need positive and any power-like condition and is suitable for many classical equations. As its corollary, we obtain the corresponding Liouville theorem and Harnack inequality.

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一类半线性椭圆方程的Liouville定理和Harnack不等式

给出了黎曼流形上一类具有（Bakry-Émery） Ricci曲率有界的半线性椭圆方程的对数梯度估计和哈纳克不等式。该非线性项不需要正的和任何幂条件，适用于许多经典方程。作为其推论，我们得到了相应的Liouville定理和Harnack不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics