W.D. Evans and Roger T. Lewis Hardy and Rellich Inequalities with Remainders (325K, pdf) ABSTRACT. In this paper our primary concern is with the establishment of weighted Hardy inequalities in $L^p(\Omega)$ and Rellich inequalities in $L^2(\Omega)$ depending upon the distance to the boundary of domains $\Omega\subset \R^n$ with a finite diameter $D(\Omega)$. Improved constants are presented in most cases.