The concavity of Rényi entropy power for the parabolic p-Laplace equations and applications

In this paper, we prove that the concavity of Rényi entropy power of positive solutions to the parabolic p-Laplace equations on compact Riemannian manifold with nonnegative Ricci curvature. As applications, we derive the improved Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-Gagliardo-Nirenberg inequalities.