Hardy inequalities with boundary singularities
Functional Analysis
2010-09-07 v1
Abstract
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.
Cite
@article{arxiv.1009.0931,
title = {Hardy inequalities with boundary singularities},
author = {Cristian Cazacu},
journal= {arXiv preprint arXiv:1009.0931},
year = {2010}
}
Comments
23 pages, 3 figures