加权黎曼流形上加权双重扩散方程的p-Rényi熵幂的凹性（英文）  

THE CONCAVITY OF p-RéNYI ENTROPY POWER FOR THE WEIGHTED DOUBLY NONLINEAR DIFFUSION EQUATIONS ON WEIGHTED RIEMANNIAN MANIFOLDS

作　　者：王宇钊 张慧廷 WANG Yu-Zhao;ZHANG Hui-Ting(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院

出　　处：《数学杂志》2019年第6期791-800,共10页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11701347)

摘　　要：本文研究了黎曼流形上熵幂的凹性问题.利用非线性Bochner公式和Bakry-émery的方法,证明了当满足曲率维数条件CD(-K, m)(K≥0, m≥n)时,对于加权双重扩散方程的正解,相关的p-Rényi熵幂是凹的,推广了之前多孔介质方程以及Ricci曲率非负情形下的结果.In this paper, we study the concavity of the entropy power on Riemannian manifolds. By using the nonlinear Bochner formula and Bakry-émery method, we prove p-Rényi entropy power is concave for positive solutions to the weighted doubly nonlinear diffusion equations on the weighted closed Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n,which generalizes the cases of porous medium equation and nonnegative Ricci curvature.

关 键 词：凹性 p-Rényi熵幂 加权双重扩散方程 m-Bakry-émery RICCI曲率 

分 类 号：O175.29[理学—数学]