El Hadji Abdoulaye Thiam
Published 2015-04-04Version 1
Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $N \geq 3$ and we let $\Sigma$ to be a closed submanifold of dimension $1 \leq k \leq 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 [8]. In particular we provide necessary and sufficient conditions for existence of minimizers.
Hardy and Hardy-Sobolev inequalities on Riemannian manifolds
On the symmetry of minimizers
Regularity and the Behavior of Eigenvalues for Minimizers of a Constrained $Q$-tensor Energy for Liquid Crystals
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