数学杂志2013，Vol.33Issue(2)：248-258,11.
光滑度量测度空间上的加权扩散方程的梯度估计
GRADIENT ESTIMATES FOR WEIGHTED DIFFUSION EQUATIONS ON SMOOTH METRIC MEASURE SPACES
摘要
Abstract
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-(E)mery 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,Vázquez 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Key words
gradient estimates/ weighted porous medium equations/ weighted fast diffusion equation/ Harnack inequality/ m-Bakry-Emery Ricci tensor分类
数理科学引用本文复制引用
王宇钊,陈文艺..光滑度量测度空间上的加权扩散方程的梯度估计[J].数学杂志,2013,33(2):248-258,11.基金项目
Supported by Fundamental Research Fund for the Central Universities. （）
