Li-Yau, Hamilton gradient and Hessian estimates for nonlinear weighted parabolic equations and applications

Abstract

This article is devoted to the study of several estimations for a positive solution to a nonlinear weighted parabolic equation on a weighted Riemannian manifold. We therefore derive new Li-Yau type and Hamilton type gradient estimates yielding several consequences. We also derive Hessian estimate and some corollaries for the same equation. Among the applications of our estimates discussed here are Harnack type inequalities, Liouville type theorems and a local time reversed Harnack inequality.