Weighted Hardy inequality with higher dimensional singularity on the boundary

Mouhamed Moustapha Fall; Fethi Mahmoudi

Weighted Hardy inequality with higher dimensional singularity on the boundary

Analysis of PDEs 2012-10-01 v2

Authors: Mouhamed Moustapha Fall , Fethi Mahmoudi

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 $1\le k\le N-2$ . 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.

Keywords

bounded domains hardy inequalities weighted inequalities

Cite

@article{arxiv.1202.0033,
  title  = {Weighted Hardy inequality with higher dimensional singularity on the boundary},
  author = {Mouhamed Moustapha Fall and Fethi Mahmoudi},
  journal= {arXiv preprint arXiv:1202.0033},
  year   = {2012}
}

Comments

26 pages

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