主要研究了C^2区域上薛定谔方程解的一些性质。对于n/(n+1)〈p≤1,Hut^p(Ω)是C^2区域Ω上的Hardy空间,f是Hut^p(Ω)上的一个分布。V(x)是薛定谔方程-div(A↓△u)+Vu=f的非负位势满足反Holder条件Bn,若对x∈Ω,弱解u满足-div(A↓△u)+Vu=f,并且它在边界δΩ的迹γu=0,得到了u的二阶导数的L^p的可积性。
This paper is devoted to research some properties of the solution of Schrodinger equation in C^2 domains. Hut^p (Ω) is the distribution of Hardy space on Ω for n/n+1〈p≤1. Given f∈Hut^p (Ω), V is a singular non-negative potential of the Schrodinger equation -div(A↓△u)+Vu=f satisfying reverse Holder condition Bn. If u is the weak solution of the Schrodinger equation --div(A↓△u)+Vu=f in Ω such that the trace γu=0 on the boundary δΩ, the L^p integraoility of the second order derivative of u will be shown in this article.