摘要
在区域Ω上考虑一类由退化向量场形成的Sch rodinger方程:∑mi,j=1Xi*(aij(x)Xju)-vu=0其中X1,…,Xm为Rn(n 3)上满足H ormander条件的实C∞向量场,X*i为Xi的形式共轭,v属于Kato类的某一类比Kηloc(Ω).并得到以下结果:若u为以上方程的弱解,则Xu 2w=∑mi=1Xiu 2w∈Klηoc(Ω).
We considered the weak solution of a class of Schrodinger equation formed by degenerated vector field：
∑i,j=1^mXi^＊（aij（x）Xju）-vu=0
where X1,…,Xm are C^∞ vector fields on R^n（n≥）3 satisfying Hormander condition, Xi^＊ is the formal adjoint of Xi, v belongs to some analogue of the kato-stummel class Kη^loc（Ω）.We obtain the following esult., let u be a weak solution of the equation ∑i,j=1^mXi^＊（aij（x）Xju）-vu=0,the ｜Xu｜^2w=∑i=1^m｜Xiu｜^2w∈Kη^loc（Ω）.
出处
《应用泛函分析学报》
CSCD
2009年第4期314-317,共4页
Acta Analysis Functionalis Applicata
基金
浙江省教育厅重点项目(Z200803357)
