HARDY-SOBOLEV INEQUALITIES WITH GENERAL WEIGHTS AND REMAINDER TERMS  

作　　者：陈志辉 沈尧天 

机构地区：[1]School of Mathematical Sciences,South China University of Technology

出　　处：《Acta Mathematica Scientia》2008年第3期469-478,共10页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation of China(10771074,10726060);the Natural Science Foundation of Guangdong Province(04020077)

摘　　要：The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.

关 键 词：Hardy-Sobolev inequality general weight best constant 

分 类 号：O178[理学—数学]