Hardy inequalities with boundary singularities

Abstract

In this work we prove some Hardy-Poincaré inequalities with quadratic singular potentials localized on the boundary of a smooth domain. Then, we consider conical domains with vertex on the singularity and we show upper and lower bounds for the corresponding optimal constants in the Hardy inequality. In particular, we prove the asymptotic behavior of the optimal constant when the slot of the cone tends to zero.

23 pages, 3 figures

Cited by in corpus (3)

• On the best constants of Hardy inequality in ${\mathbb{R}}^{n-k}\times ({\mathbb{R}}_{+}{)}^k$ and related improvements
• The method of super-solutions in Hardy and Rellich type inequalities in the $L^2$ setting: an overview of well-known results and short proofs
• Solutions of nonhomogeneous equations involving Hardy potentials with singularities on the boundary