Gradient estimates for a weighted nonlinear parabolic equation and applications

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.

Keywords

• gradient estimates
• bakry-émery tensor
• parabolic equation
• liouville theorem
• heat kernel
• harnack inequality
• 35k55
• 53c21
• 35b53
• 58j38