关于L-上调和函数的强极值原理

Strong Maximun Principle for L-Superharmonic Functions

在R^n(n≥2)的子区域Ω上,若f≠0是关于严格椭圆的二阶线性半微分算子■■■负上■和函数且b∈■Ω有邻域V使得■Ω∩■是C^1流形,■末对任意以b为顶点的Stolz■■D■Ω,恒有,此处ρ(x,■Ω)=inf(‖x-y‖;y∈■Ω),类似的结论对于较一般的Riemann流形如■空间的妇■■边成立,上述可否成用法■导数描述的Hopf型强极值原理一种推广定式。

Let Ω be a domain on Rn(n≥2) and L be a strictiy elliptic partial differential operator on Ωwith Haider continuous coeffients, This paper proves that if f≥0 (f≠0) is a superharmoaic function with respect to the operator L on Ω, then for any b∈ Ω which has a neighbo-hood V such that Ω V is a C1 manifold and for any Stolz domain D at b, D Ω, we have wherep( x, Ω) =inf{||x-y||; y∈ Ω||}; moreover, an analogue conclusion is also valid in a domain of the Riemann manifold which is an E-space, These results can be viewed as a generalization of E. Hopf maximum principle.