Gradient estimates for weighted harmonic function with Dirichlet boundary condition. (December 2021)

• Record Type: Journal Article
• Authors: Dung, Nguyen Thac; Wu, Jia-Yong
• Is Part Of: Nonlinear analysis. Volume 213(2021)
• Publication Date: 2021-12
• Subjects: primary 58J05 -- secondary 35B53; Smooth metric measure space -- Bakry–Émery Ricci curvature -- Manifold with boundary -- Harmonic function -- Gradient estimate -- Liouville theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112498
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .