Logarithmic Harnack inequalities and differential Harnack estimates for p-Laplacian on Riemannian manifolds

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 estimates for positive solution to p-Laplacian parabolic equation with logarithmic nonlinearity. These results generalize the works of Chung-Yau, F.-Y. Wang and X. Cao ect. for the classic L2 case.Mathematics Subject Classification (2020). 58J05; 58J65