Gradient Estimates for a Nonlinear Parabolic Equation on Complete Smooth Metric Measure Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Fanqi Zeng
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Gradient Estimates ◽  
Metric Measure Spaces ◽  
Nonlinear Parabolic ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces

scholarly journals Liouville theorems and elliptic gradient estimates for a nonlinear parabolic equation involving the Witten Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ali Taheri
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Gradient Estimates ◽  
Elliptic Type ◽  
Liouville Type ◽  
Witten Laplacian ◽  
Smooth Metric Measure Space ◽  
Nonlinear Parabolic ◽  
Global Estimates ◽  
Liouville Type Results

Abstract In this paper, we establish local and global elliptic type gradient estimates for a nonlinear parabolic equation on a smooth metric measure space whose underlying metric and potential satisfy a ( k , m ) {(k,m)} -super Perelman–Ricci flow inequality. We discuss a number of applications and implications including curvature free global estimates and some constancy and Liouville type results.

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