Gradient estimates and Liouville type theorems for (p-1)p-1Δpu+aup-1logup-1=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p-1)^{p-1}\Delta _pu+au^{p-1}\log u^{p-1}=0$$\end{document} on Riemannian manifolds

被引:0
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作者
Bingqing Ma
Mingfang Zhu
机构
[1] Henan Normal University,Department of Mathematics
关键词
-Laplace; Liouville theorem; Positive smooth solution; Primary 58J05; Secondary 58J35;
D O I
10.1007/s00013-021-01639-4
中图分类号
学科分类号
摘要
In this paper, we study gradient estimates of positive smooth solutions to the p-Laplace equation (p-1)p-1Δpu+aup-1logup-1=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} (p-1)^{p-1}\Delta _pu+au^{p-1}\log u^{p-1}=0, \end{aligned}$$\end{document}which is related to the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-log-Sobolev constant on Riemannian manifolds, where a is a nonzero constant. As applications, some Liouville type results are provided.
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页码:557 / 567
页数:10
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