Gradient estimates for positive weak solution to Δpu + auσ=0 on Riemannian manifolds

被引：2

作者：

Huang, Guangyue ^{[1
]}

Guo, Qi ^{[1
]}

Guo, Lujun ^{[1
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 533卷 / 02期

关键词：

Gradient estimate; p-Laplacian; Harnack inequality; LAPLACIAN LICHNEROWICZ EQUATION; LIOUVILLE TYPE THEOREMS; P-HARMONIC FUNCTIONS; ELLIPTIC EQUATION;

D O I：

10.1016/j.jmaa.2023.128007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study gradient estimates for positive weak solutions to the following p -Laplacian equation Delta(p)u + au(sigma) = 0on a Riemannian manifold, where p > 1 and a, sigma are two nonzero real constants. By virtue of the Morser iteration technique, we derive some gradient estimates, which show that when the Ricci curvature is nonnegative, the above equation does not admit positive weak solutions under some scopes of p.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：16

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