GRADIENT ESTIMATES AND ENTROPY FORMULAE FOR WEIGHTED p-HEAT EQUATIONS ON SMOOTH METRIC MEASURE SPACES  

作　　者：王宇钊 杨杰 陈文艺 

机构地区：[1]School of Mathematics and Statistics, Wuhan University [2]College of Mathematics and System Science, Xinjiang University

出　　处：《Acta Mathematica Scientia》2013年第4期963-974,共12页数学物理学报（B辑英文版）

基　　金：supported by the Fundamental Research Fund for the Central Universities

摘　　要：Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].

关 键 词：gradient estimates weighted p-heat equation entropy monotonicity formula m-Bakry-t^mery Ricci curvature 

分 类 号：O175[理学—数学] O551.3[理学—基础数学]