Weighted Hardy inequality with higher dimensional singularity on the boundary

الأصل · EN

Let Ω be a smooth bounded domain in Rⁿ with N≥ 3 and let Σₖ be a closed smooth submanifold of δΩ of dimension 1≤ k≤ N-2. In this paper we study the weighted Hardy inequality with weight function singular on Σₖ. In particular we provide sufficient and necessary conditions for existence of minimizers.