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math.DG2021★ 1 cited
Sharp gradient estimates on weighted manifolds with compact boundary
Ha Tuan Dung, Nguyen Thac Dung, Jia-Yong Wu
In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we p…
math.DG2021
Gradient estimates for weighted harmonic function with Dirichlet boundary condition
Nguyen Thac Dung, Jia-Yong Wu
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 inf…