Weighted Hardy inequality with higher dimensional singularity on the boundary

Details Weighted Hardy inequality with higher dimensional singularity on the boundary Weighted Hardy inequality with higher dimensional singularity on the boundary

2012-01-31

arxiv.org/abs/1202.0033v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

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.

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