Weighted Hardy inequality on Riemannian manifolds

2015/04/04 by Thiam, El Hadji Abdoulaye
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.00972

Abstract

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

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