光滑度量测度空间上的加权扩散方程的梯度估计(英文)  

GRADIENT ESTIMATES FOR WEIGHTED DIFFUSION EQUATIONS ON SMOOTH METRIC MEASURE SPACES

作　　者：王宇钊[1] 陈文艺[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2013年第2期248-258,共11页Journal of Mathematics

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

摘　　要：本文主要考虑了一类加权非线性扩散方程正解的梯度估计.在m-维Bakry-meryRicci曲率下有界的假设下,得到加权多孔介质方程(γ>1)正解的Li-Yau型梯度估计,此外对于加权快速扩散方程(0<γ<1),证明了Hamilton型椭圆梯度估计,结论分别推广了Lu,Ni,Va′zquezandVillani在文[1]和Zhu在文[2]中的结果.In this paper, we consider gradient estimates for the positive solutions to the nonlinear weighted diffusion equations. Under the assumption that the m-dimensional Bakry- ′ Emery Ricci curvature bounded below by a non-positive constant, we derive a Li-Yau type gradient estimate for postive solution of weighted porous medium equations （γ 1） and also prove a Hamilton type elliptic gradient estimate for weighted fast diffusion equation （0 γ 1）, which generalize the ones of Lu, Ni, Va′zquez and Villani in [1] and Zhu in [2].

关 键 词：梯度估计 加权多孔介质方程 加权快速扩散方程 HARNACK不等式 m-Bakry-Emery Ricci曲率张量 

分 类 号：O186.12[理学—数学] O175.29[理学—基础数学]