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 space

Authors: Xiaoshan Wang ; Linfen Cao

    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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