[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b180639

GRADIENT ESTIMATES OF A NONLINEAR ELLIPTIC EQUATION FOR THE V -LAPLACIAN

Zeng, Fanqi (School of Mathematics and Statistics Xinyang Normal University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 853-865 More about this Journal

Abstract

In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: ${\Delta}_Vu+cu^{\alpha}=0$ , where c, ${\alpha}$ are two real constants and $c{\neq}0$ . 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- ${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].

Keywords

gradient estimate; nonlinear elliptic equation; Bakry- ${\acute{E}}mery$ Ricci curvature;

Citations & Related Records

Reference

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