Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3159
Keywords
Gradient estimates, $V$-Laplacian, Riemannian manifolds, Bakry-Emery Ricci curvature
First Page
1294
Last Page
1301
Recommended Citation
YIHUA, D (2022). Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian on noncompact Riemannian manifolds. Turkish Journal of Mathematics 46 (4): 1294-1301. https://doi.org/10.55730/1300-0098.3159
