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

Stathis Filippas; Achilles Tertikas; Jesper Tidblom

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

Analysis of PDEs 2009-11-06 v1 Spectral Theory

Authors: Stathis Filippas , Achilles Tertikas , Jesper Tidblom

Abstract

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.

Keywords

sobolev inequalities hardy inequalities inequalities

Cite

@article{arxiv.0911.0942,
  title  = {Optimal Hardy-Sobolev-Maz'ya inequalities with multiple interior singularities},
  author = {Stathis Filippas and Achilles Tertikas and Jesper Tidblom},
  journal= {arXiv preprint arXiv:0911.0942},
  year   = {2009}
}

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