Gradient estimates of a general porous medium equation for the V-Laplacian

Abstract

In this paper, we consider the gradient estimates for the positive solutions to the following porous medium equation

u_t = Δ_Vu^m,

where m > 1. We obtain Li-Yau type bounds of the above equation on Riemannian manifolds with Bakry-Emery type curvature bounded from below, which improves the estimates in [25] and covers the ones in [22, 18, 19, 27].