Optimal Hardy-Sobolev-Maz'ya inequalities with multiple interior singularities

Details Optimal Hardy-Sobolev-Maz'ya inequalities with multiple interior singularities Optimal Hardy-Sobolev-Maz'ya inequalities with multiple interior singularities

2009-11-04

arxiv.org/abs/0911.0942v1

Mathematics

Analysis of PDEs

Scientific paper

In this article we first establish a complete characterization of Hardy's
inequalities in $\mathbb{R}^n$ involving distances to different codimension
subspaces. In particular the corresponding potentials have strong interior
singularities. We then provide necessary and sufficient conditions for the
validity of Hardy-Sobolev-Maz'ya inequalities with optimal Sobolev terms.

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