scholarly journals Gradient estimates for the $p$-Laplacian Lichnerowicz equation on smooth metric measure spaces

2018 ◽  
Vol 146 (12) ◽  
pp. 5451-5461 ◽  
Author(s):  
Liang Zhao ◽  
Dengyun Yang
Keyword(s):  
Gradient Estimates ◽  
Metric Measure Spaces ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces ◽  
Lichnerowicz Equation

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>

Sign in / Sign up

Export Citation Format

Share Document