| 一类次椭圆方程弱解的正则性 |
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| 引用本文： | 林荣斐,吕杰林.一类次椭圆方程弱解的正则性[J].应用泛函分析学报,2009,11(4):314-317. |
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| 作者姓名： | 林荣斐 吕杰林 |
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| 作者单位： | 1. 浙江台州学院数学系,临海,317000
2. 浙江商业职业技术学院,杭州,310014 |
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| 基金项目： | 浙江省教育厅重点项目 |
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| 摘 要： | 在区域Ω上考虑一类由退化向量场形成的Schrodinger方程：
∑i,j=1^mXi^＊（aij（x）Xju）-vu=0
其中X1,…,Xm为R^n（n≥）3上满足Hormander条件的实C^∞向量场，Xi^＊为Xi的形式共轭，v属于Kato类的某一类比Kη^loc（Ω）.并得到以下结果：若u为以上方程的弱解，则｜Xu｜^2w=∑i=1^m｜Xiu｜^2w∈Kη^loc（Ω）.
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| 关 键 词： | 退化椭圆方程 Kato类 Green函数 |
Regularity for Weak Solutions of a Class of Subelliptic Equations |
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| LIN Rong-fei,LV Jie-lin.Regularity for Weak Solutions of a Class of Subelliptic Equations[J].Acta Analysis Functionalis Applicata,2009,11(4):314-317. |
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| Authors: | LIN Rong-fei LV Jie-lin |
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| Institution: | 1. Department of Mathematics, Taizhou University, Linhai 317000, China; 2. Vocational College of Commerce, Hangzhou 310014, China) |
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| Abstract: | We considered the weak solution of a class of Schrodinger equation formed by degenerated vector field∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0)where X_1,…,X_m are C~∞ vector fields on R~n (n≥3) satisfying Hormander condition, X_t~* is the formal adjoint of X_t. v belongs to some analogue of the kato-stummel class K_η~(loc)(Ω). We obtain the following result: let u be a weak solution of the equation ∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0),then ｜Xu｜~2w=∑_(i=1)~m｜X_i,u｜~2w∈K_η~(loc)(Ω). |
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| Keywords: | degenerate elliptic equation Kato class Green function |
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