Gradient estimates for weighted harmonic function with Dirichlet boundary condition
Differential Geometry
2021-07-14 v2
Abstract
We prove a Yau's type gradient estimate for positive -harmonic functions with the Dirichlet boundary condition on smooth metric measure spaces with compact boundary when the infinite dimensional Bakry-Emery Ricci tensor and the weighted mean curvature are bounded below. As an application, we give a Liouville type result for bounded -harmonic functions with the Dirichlet boundary condition. Our results do not depend on any assumption on the potential function .
Cite
@article{arxiv.2105.06205,
title = {Gradient estimates for weighted harmonic function with Dirichlet boundary condition},
author = {Nguyen Thac Dung and Jia-Yong Wu},
journal= {arXiv preprint arXiv:2105.06205},
year = {2021}
}
Comments
10 pages, 1 figure,final version, accepted by Nonlinear Analysis