scholarly journals Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces

2017 ◽  
Vol 155 (3-4) ◽  
pp. 471-501 ◽  
Author(s):  
Nguyen Thac Dung ◽  
Nguyen Ngoc Khanh ◽  
Quốc Anh Ngô
Keyword(s):  
Gradient Estimates ◽  
Heat Equations ◽  
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>

Jump processes and nonlinear fractional heat equations on metric measure spaces

2006 ◽  
Vol 279 (1-2) ◽  
pp. 150-163 ◽  
Author(s):  
Jiaxin Hu ◽  
Martina Zähle
Keyword(s):  
Jump Processes ◽  
Heat Equations ◽  
Metric Measure Spaces ◽  
Measure Spaces
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