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].
出处
《数学杂志》
CSCD
北大核心
2013年第2期248-258,共11页
Journal of Mathematics
基金
Supported by Fundamental Research Fund for the Central Universities
