Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian on noncompact Riemannian manifolds

Authors

DENG YIHUA

DOI

10.55730/1300-0098.3159

Abstract

In this paper, we consider gradient estimates for positive solutions to the following equation $$\triangle_V u+au^p\log u=0$$ on complete noncompact Riemannian manifold with $k$-dimensional Bakry-Emery Ricci curvature bounded from below. Using the Bochner formula and the Cauchy inequality, we obtain upper bounds of $ \nabla u $ with respect to the lower bound of the Bakry-Emery Ricci curvature.

Keywords

Gradient estimates, $V$-Laplacian, Riemannian manifolds, Bakry-Emery Ricci curvature

First Page

1294

Last Page

1301

Recommended Citation

YIHUA, DENG (2022) "Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian on noncompact Riemannian manifolds," Turkish Journal of Mathematics: Vol. 46: No. 4, Article 12. https://doi.org/10.55730/1300-0098.3159
Available at: https://journals.tubitak.gov.tr/math/vol46/iss4/12