Open AccessSharp gradient estimates on weighted manifolds with compact boundary
Author(s) -
Ha Tuan Dung,
Nguyễn Tiến Dũng,
Jia-Yong Wu
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021148
Subject(s) - boundary (topology) , mathematics , measure (data warehouse) , compact space , metric (unit) , mathematical analysis , dirichlet boundary condition , infinity , dirichlet distribution , pure mathematics , boundary value problem , computer science , operations management , database , economics
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 prove Liouville theorems for ancient solutions satisfying the Dirichlet boundary condition and some sharp growth restriction near infinity. Our results can be regarded as a refinement of recent results due to Kunikawa and Sakurai.