Liouville theorems and gradient estimates for a nonlinear elliptic equation

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• 作者：Lin Feng Wang¹ ; ^{wlf711178@126.com" class="auth_mail" title="E-mail the corresponding author} ; ^{wlf711178@ntu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53C21 ; 53C25
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 January 2016
• 年：2016
• 卷：260
• 期：1
• 页码：567-585
• 全文大小：267 K

文摘

In this paper we establish gradient estimates for positive solutions to the equation on any smooth metric measure space whose m  -Bakry–Émery curvature is bounded from below by −(m−1)K$-(m-1)K$ with K≥0$K\ge 0$. These estimates imply Liouville theorems for (0.1). When p→1$p\to 1$, our main theorem reduces to the gradient estimate of Wang (2010) [9]. As applications, several Harnack inequalities are obtained.