Hardy-Poincare' inequalities with boundary singularities

Abstract

Let $Ø$ be a bounded domain in ${\mathbb{R}}^N$ with $0\in\deØ$ and $N\ge 2$. In this paper we study the Hardy-Poincaré inequality for maps in $H_0^1(\Omega )$. In particular we give sufficient and some necessary conditions so that the best constant is achieved.