Gradient estimates for a nonlinear elliptic equation on a smooth metric measure spaceArticle
Authors: Xiaoshan Wang 1; Linfen Cao 2
NULL##NULL
Xiaoshan Wang;Linfen Cao
- 1 Luoyang Normal University
- 2 Henan Normal University
Let (M, g, e −f dv) be a smooth metric measure space. We consider local gradient estimates for positive solutions to the following elliptic equation ∆ f u + au log u + bu = 0 where a, b are two real constants and f be a smooth function defined on M. As an application, we obtain a Liouville type result for such equation in the case a < 0 under the m-dimensions Bakry-Émery Ricci curvature.
Volume: Volume 32 (2024), Issue 1
Published on: February 27, 2023
Accepted on: February 13, 2023
Submitted on: February 13, 2023
Keywords: [MATH]Mathematics [math], [en] 2010 Mathematics Subject Classification. Primary 58J35 Secondary 35B45 gradient estimates nonlinear equation m-dimensions Bakry-Émery Ricci curvature Liouville type property, 2010 Mathematics Subject Classification. Primary 58J35, Secondary 35B45 gradient estimates, nonlinear equation, m-dimensions Bakry-Émery Ricci curvature, Liouville type property