scholarly journals Gradient estimates for some evolution equations on complete smooth metric measure spaces

2020 ◽  
Vol 96 (1-2) ◽  
pp. 1-21
Author(s):  
Nguyen Thac Dung ◽  
Kieu Thi Thuy Linh ◽  
Ninh Van Thu
Keyword(s):  
Evolution Equations ◽  
Gradient Estimates ◽  
Metric Measure Spaces ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces

scholarly journals Sharp gradient estimates on weighted manifolds with compact boundary

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ha Tuan Dung ◽  
Nguyen Thac Dung ◽  
Jiayong Wu
Keyword(s):  
Dirichlet Boundary ◽  
Gradient Estimates ◽  
Metric Measure Spaces ◽  
Liouville Theorems ◽  
Ancient Solutions ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces ◽  
Sharp Growth ◽  
Weighted Manifolds ◽  
Compact Boundary

<p style='text-indent:20px;'>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.</p>

A Liouville theorem for weightedp−Laplace operator on smooth metric measure spaces

2016 ◽  
Vol 40 (4) ◽  
pp. 992-1002 ◽  
Author(s):  
Lin Feng Wang ◽  
Ze Yu Zhang ◽  
Liang Zhao ◽  
Yu Jie Zhou
Keyword(s):  
Laplace Operator ◽  
Liouville Theorem ◽  
Metric Measure Spaces ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces
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