Gradient estimates for the p-Laplace heat equation under the Ricci flow

Abstract

We establish space-only gradient estimates for positive continuous weak solutions to the p-Laplace heat equation on some complete manifolds evolving under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at different points.

Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity

“…Recently, for the singular diffusion case 1 < p < 2 and for q = p, F. Wang [20] established gradient estimates similar to (1.2) for smooth, upper bounded, local solutions to (1.1) on a closed manifolds or on complete noncompact Riemannian manifolds evolving under a Ricci flow. These estimates are of the form:…”