Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 610530, 10 pages
doi:10.1155/2009/610530
Research Article

An Improved Hardy-Rellich Inequality with Optimal Constant

Ying-Xiong Xiao1 and Qiao-Hua Yang2

1School of Mathematics and Statistics, Xiaogan University, Xiaogan, Hubei 432000, China
2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received 25 May 2009; Accepted 11 September 2009

Academic Editor: Siegfried Carl

Copyright © 2009 Ying-Xiong Xiao and Qiao-Hua Yang. 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 show that a Hardy-Rellich inequality with optimal constants on a bounded domain can be refined by adding remainder terms. The procedure is based on decomposition into spherical harmonics.