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.
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.