Xiaoshan Wang ; Linfen Cao - Gradient estimates for a nonlinear elliptic equation on a smooth metric measure space

cm:10951 - Communications in Mathematics, February 27, 2023, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.10951
Gradient estimates for a nonlinear elliptic equation on a smooth metric measure spaceArticle

Authors: Xiaoshan Wang 1; Linfen Cao 2

  • 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: 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,[MATH]Mathematics [math]

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