Hardy inequalities with boundary singularities

Details Hardy inequalities with boundary singularities Hardy inequalities with boundary singularities

2010-09-05

arxiv.org/abs/1009.0931v1

Mathematics

Functional Analysis

23 pages, 3 figures

Scientific paper

In this work we prove some Hardy-Poincar\'{e} 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.

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