数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 621-626.

• 论文 • 上一篇    下一篇

加权Hardy-Sobolev不等式及其应用

张书陶   

  1. 中国计量学院数学系 杭州 310018
  • 收稿日期:2011-09-11 修回日期:2012-10-08 出版日期:2013-08-25 发布日期:2013-08-25
  • 基金资助:

    国家自然科学基金(11201443)和浙江省自然科学基金(Y6110118)资助

Weighted Hardy-Sobolev Inequality and Its Application

 ZHANG Shu-Tao   

  1. Department of Mathematics, College of Science, China Jiliang University, Hangzhou 310018
  • Received:2011-09-11 Revised:2012-10-08 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    国家自然科学基金(11201443)和浙江省自然科学基金(Y6110118)资助

摘要:

受Chern等讨论Caffarelli-Kohn-Nirenberg不等式极小值问题中函数变换的启发, 该文获得一类加权的Hardy-Sobolev不等式; 作为应用, 当1<p<n时, 为Caffarelli-Kohn-Nirenberg不等式提供一个新的、简洁的证明方法.

关键词: 加权Hardy-Sobolev不等式, Caffarelli-Kohn-Nirenberg不等式

Abstract:

For discussing the minimize problem of Caffarelli-Kohn-Nirenberg inequality  with p=2, Chern and Lin[4] introduce a class of function transformation. Inspired by the transformation, a class of weighted Hardy-Sobolev inequality on Rn is obtained. As an application, a new and concise proof is given for Caffarelli-Kohn-Nirenberg inequality with 1<p<n.

Key words: Weighted Hardy-Sobolev inequality, Caffarelli-Kohn-Nirenberg inequality

中图分类号: 

  • 26D10