Let $\O$ be a smooth bounded domain in $\R^N$ with $N\ge 1$. In this paper we study the Hardy-Poincar\'e inequalities with weight function singular at the boundary of $\O$. In particular we give sufficient conditions so that the best constant is achieved.
On the Hardy-Poincaré inequality with boundary singularities
Hardy-Poincare' inequalities with boundary singularities
On the boundary terms in Hardy's inequalities for $W^{1,p}$ functions
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