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arXiv · 2105.06205

Gradient estimates for weighted harmonic function with Dirichlet boundary condition

Nguyen Thac Dung·Jia-Yong Wu
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Abstract

We prove a Yau's type gradient estimate for positive $f$-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 $f$-harmonic functions with the Dirichlet boundary condition. Our results do not depend on any assumption on the potential function $f$.

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Nguyen Thac Dung, Jia-Yong Wu. 2021-05-13. Gradient estimates for weighted harmonic function with Dirichlet boundary condition. https://arxiv.org/abs/2105.06205

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