一类分数阶椭圆方程解的渐近行为

Asymptotic Behavior of Solution to a Class of Fractional Elliptic Equations

应用Stampacchia方法,研究低阶项的正则化效应和Hardy位势对如下分数阶拉普拉斯方程解的渐近行为的影响{(-△)su-λu/|x|<sup>2s+up=f(x),x∈Ω,u>0,x∈Ω,u=0,x∈RN\Ω,其中(-△)s是分数阶Laplacian算子,s∈(0,1)且N> 2s,ΩRN是具有Lipschitz边界的有界光滑区域且0∈Ω.

In this paper,we study the effect of the Hardy potedtial to a class.of nonlocal elliptic problems with lower order terms:{(-△)^su-λ u/|x|^2s+u^p=f(x),x∈Ω u>0,x∈Ω,u=0,x∈R^N\Ω,where(-△)^s is the fractional Laplacian operator,s∈(0,1) and N>2s,Ω R^N is a bounded domain'with 'Lipschitz boundary such that 0∈Ω.