与广义Baouendi-Grushin向量场相联系的Hardy不等式及其应用(英文)  

Hardy Inequalities and Applications Related to Generalized Baouendi-Grushin Vector Fields

作　　者：窦井波[1] 钮鹏程[1] 

机构地区：[1]西北工业大学应用数学系,西安陕西710072

出　　处：《数学进展》2008年第3期321-331,共11页Advances in Mathematics（China）

基　　金：NSFC(No.10371099).

摘　　要：本文建立一类与广义Baouendi-Grushin向量场联系的Hardy不等式.采用的技巧是延伸欧氏空间上的散度定理推出的基本积分不等式和选定适当的向量场.Hardy不等式相应的最佳常数也得到证明.本文结果包括了已有广义Baouendi-Grushin向量场的Hardy不等式.作为应用,讨论了由Baouendi-Grushin向量场构成-退化次椭圆算子的一些性质和刻画了这类向量场构成的非线性算子的一个正解.In this paper we establish a class of Hardy inequalities related to the generalized Baouendi-Grushin vector fields from another view. Our technique is based on an extension of an elementary integral inequality in the Euclidean space by the generalized divergence theorem, and then the choice of suitable vector fields. The best constant is also discussed. Our results contain the well known Hardy inequalities for the class of vector fields. As immediate consequences, we discuss some properties for p-degenerate subelliptic operator and characterize a positive solutions of the nonlinear operator constructed by generalized Baouendi-Grushin vector fields.

关 键 词：广义Baouendi—GruShin向量场 HARDY不等式 最佳常数 

分 类 号：O178[理学—数学] O175.1[理学—基础数学]