Gradient estimates for a parabolic 𝑝-Laplace equation with logarithmic nonlinearity on Riemannian manifolds

Abstract

In this paper, we study gradient estimates for a parabolic p p -Laplace equation with logarithmic nonlinearity, which is related to the L p L^p -log-Sobolev constant on Riemannian manifolds. We prove a global Li-Yau type gradient estimate and a Hamilton type gradient estimate for positive solutions to a parabolic p p -Laplace equation with logarithmic nonlinearity on compact Riemannian manifolds with nonnegative Ricci curvature. As applications, the corresponding Harnack inequalities are derived.