论文标题
在完全非策略度量测量空间上的非线性方程的梯度估计值紧凑
Gradient estimates of nonlinear equation on complete noncompact metric measure space with compact boundary
论文作者
论文摘要
在本文中，首先，我们研究了以下方程\ begin {equation*}Δ_ξ（u） - \ partial_t u- q u = a（u = a（u），t \ in（ - \ infty，\ infty，\ infty）\ end end e e e e e e e e e e demant \ in（\ infty，\ infty）\ end end end e e e e e e^y = a（m， ，其中$Δ_ξ=δ+\ left \ langle \ nabla \ cdot，\ nablaξ\ right \ rangle $。对于此方程，我们得出了Li-YAU类型梯度估计值和汉密尔顿的类型梯度估计。其次，我们获得了以下椭圆类型方程的阳性解的梯度估计\ begin {qore}Δ_ξ（u） - q u = a（u = a（u）\ end \ end {equation}上的完整的非合理度量度量空间$（m，g，e^{ - e^{ - e^{ - e^{ - E^{ - ξ} \ Mathrm {d} v_g {d} v_g）$。
In this paper, firstly, we study gradient estimates for positive solution of the following equation \begin{equation*} Δ_ξ(u)-\partial_t u- q u =A(u),t\in (-\infty,\infty) \end{equation*} on metric measure space $ (M,g,e^{-ξ}\mathrm{d} v_g)$ with boundary , where $ Δ_ξ=Δ+\left \langle \nabla\cdot , \nabla ξ\right \rangle $. For this equation, we derive Li-Yau type gradient estimates and Hamilton's type gradient estimates. Secondly, we obtain gradient estimates for positive solution of the following elliptical type equation \begin{equation} Δ_ξ(u)- q u =A(u)\end{equation} on complete noncompact metric measure space $(M,g,e^{-ξ}\mathrm{d} v_g)$ with boundary.
