论文标题
多孔培养基方程的梯度估计和具有紧凑边界的完整非脉冲度量测量空间上的快速扩散类型方程
Gradient estimates for the porous medium type equations and fast diffusion type equations on complete noncompact metric measure space with compact boundary
论文作者
论文摘要
在本文中，我们得出了以下方程式\ begin \ begin {等式*} \ begin {split} u_T =δ_e_ξp+λu+a（u），\ end eend {split {split} \ end eent {equation {equation {equal {equation*}，在完全的nontonnontonpopact $ $（$）$ quate $（e End）中，紧凑边界。我们还将给出方程\ begin {等式*}Δ_ξ（u^p）+λu+a（u）= 0，\ end eend {equation*}的局部梯度估计。
In the paper, we derive Li-Yau gradient estimates and Souplet Zhang type estimates of the following equation \begin{equation*} \begin{split} u_t= Δ_ξp+λu+A(u) , \end{split} \end{equation*} on complete noncompact metric measure space $ (M, g,e^{-ξ}dv_g) $ with compact boundary. We will also give the local gradient estimates of the equation \begin{equation*} Δ_ξ(u^p)+λu+A(u)=0, \end{equation*} on complete noncompact manifold with compact boundary.
