Weighted Hardy inequality with higher dimensional singularity on the boundary
Abstract
Let $\Omega$ be a smooth bounded domain in $\mahbb R^N$ with $N\ge 3$ and let $\Sigma_k$ be a closed smooth submanifold of $\delta \Omega$ of dimension $1\le k\le N2$. In this paper we study the weighted Hardy inequality with weight function singular on $\Sigma_k$. In particular we provide sufficient and necessary conditions for existence of minimizers.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 arXiv:
 arXiv:1202.0033
 Bibcode:
 2012arXiv1202.0033M
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 26 pages