Gradient estimates on the weighted p-Laplace heat equation.

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p -Laplace heat equation when the m -Bakry–Émery curvature is bounded from below by − K for some constant K ≥ 0 . When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p -Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0 , and reduce to the Davies, Hamilton and Li–Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2 . [ABSTRACT FROM AUTHOR]