Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian
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In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $$\Delta_{V}u+cu^{\alpha}=0,$$ where $c$, $\alpha$ are two real constants and $c\neq0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-\'{E}mery Ricci curvature bounded from below, which generalize some results of \cite{MHL2017}.
Abstract
In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $$\Delta_{V}u+cu^{\alpha}=0,$$ where $c$, $\alpha$ are two real constants and $c\neq0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-\'{E}mery Ricci curvature bounded from below, which generalize some results of \cite{MHL2017}.
참고문헌 (12)
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