Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (4): 621-626.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 26D10
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