Weighted Hardy inequality on Riemannian manifolds

Abstract

Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $N\ge 3$ and we let $\Sigma$ to be a closed submanifold of dimension $1\le k\le N-2.$ In this paper we study existence and non-existence of minimizers of Hardy inequality with weight function singular on $\Sigma$ within the framework of Brezis-Marcus-Shafrir. In particular we provide necessary and sufficient conditions for existence of minimizers.

arXiv commentin Communication in Contemporary Mathematics, 2015