Logarithmic Harnack inequalities and gradient estimates for nonlinear p-Laplace equations on weighted Riemannian manifolds

Abstract

In this paper, we prove the logarithmic Harnack inequalities for L^p-Log-Sobolev function on n-dimensional weighted Riemannian manifolds with m-Bakry-Émery Ricci curvature bounded below by -K (m ≥ n, K ≥ 0). Under the assumption of nonnegative m-Bakry-Émery Ricci curvature, we obtain a global Li-Yau type gradient estimate and a Hamilton type estimate for the positive solutions to the weighted parabolic p-Laplace equation with logarithmic nonlinearity. As applications, the corresponding Harnack inequalities are derived.