Abstract
In this paper, we study logarithmic Harnack inequalities and differential Harnack estimates for p-Laplacian on Riemannian manifolds. We prove the logarithmic Harnack inequalities for Lp-log-Sobolev functions on Riemannian manifolds with Ricci curvature bounded below, which is related to the Lp-log-Sobolev constant. We obtain a new Li-Yau type differential Harnack estimate for the positive solution to p-Laplacian parabolic equation with logarithmic nonlinearity. These results generalize the works of Chung-Yau, F.-Y. Wang and X. Cao etc. for the classic L2 case.
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