完备非紧带紧边界的度量测度空间上多孔介质型方程与快扩散型方程的梯度估计
微分几何
2024-08-16 v2 偏微分方程分析
摘要
在本文中，我们推导了以下方程 \begin{equation*} \begin{split} u_t= \Delta_\xi p+\lambda u+A(u) , \end{split} \end{equation*} 在带紧边界的完备非紧度量测度空间 上的Li-Yau梯度估计与Souplet Zhang型估计。我们还将给出方程 \begin{equation*} \Delta_\xi(u^p)+\lambda u+A(u)=0, \end{equation*} 在带紧边界的完备非紧流形上的局部梯度估计。
引用
@article{arxiv.2210.00224,
title = {Gradient estimates for the porous medium type equations and fast diffusion type equations on complete noncompact metric measure space with compact boundary},
author = {Xiangzhi Cao},
journal= {arXiv preprint arXiv:2210.00224},
year = {2024}
}
备注
The main theorem of this paper is not worth to publish, since the conditions is too strong and meaningless