Gradient estimates for weighted harmonic function with Dirichlet boundary condition
نویسندگان
چکیده
We prove a Yau’s type gradient estimate for positive f-harmonic functions with the Dirichlet boundary condition on smooth metric measure spaces compact when infinite dimensional Bakry–Emery Ricci tensor and weighted mean curvature are bounded below. As an application, we give Liouville result condition. Our results do not depend any assumption potential function f.
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ژورنال
عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications
سال: 2021
ISSN: ['1873-5215', '0362-546X']
DOI: https://doi.org/10.1016/j.na.2021.112498