scholarly journals Gradient Estimates and Harnack Inequality for a Nonlinear Parabolic Equation on Complete Manifolds

2013 ◽  
Vol 1 (4) ◽  
pp. 437-464
Author(s):  
Jiaxian Wu ◽  
Yi-Hu Yang
Keyword(s):  
Parabolic Equation ◽  
Harnack Inequality ◽  
Nonlinear Parabolic Equation ◽  
Gradient Estimates ◽  
Nonlinear Parabolic ◽  
Complete Manifolds

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.

scholarly journals Gradient estimates for a weighted nonlinear parabolic equation and applications

2020 ◽  
Vol 18 (1) ◽  
pp. 1150-1163
Author(s):  
Abimbola Abolarinwa ◽  
Nathaniel K. Oladejo ◽  
Sulyman O. Salawu
Keyword(s):  
Parabolic Equation ◽  
Riemannian Manifold ◽  
Nonlinear Parabolic Equation ◽  
Type Theorem ◽  
Gradient Estimates ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harnack Inequalities ◽  
Nonlinear Parabolic ◽  
Lower Boundedness

Abstract This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.

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