Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 419845, 24 pages
doi:10.1155/2009/419845
Research Article

Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms

Yaotian Shen and Zhihui Chen

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received 18 December 2008; Accepted 10 August 2009

Academic Editor: Panayiotis Siafarikas

Copyright © 2009 Yaotian Shen and Zhihui Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a class of sharp Hardy-Sobolev inequality, where the weights are functions of the distance from a surface. It is proved that the Hardy-Sobolev inequality can be successively improved by adding to the right-hand side a lower-order term with optimal weight and constant.