Critical Hardy--Sobolev Inequalities

S. Filippas; V. Maz'ya; A. Tertikas

Critical Hardy--Sobolev Inequalities

Analysis of PDEs 2007-05-23 v1 Functional Analysis

Authors: S. Filippas , V. Maz'ya , A. Tertikas

Abstract

We consider Hardy inequalities in $I R^n$ , $n \geq 3$ , with best constant that involve either distance to the boundary or distance to a surface of co-dimension $k<n$ , and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm.

Keywords

sobolev inequalities hardy inequalities inequalities

Cite

@article{arxiv.math/0611484,
  title  = {Critical Hardy--Sobolev Inequalities},
  author = {S. Filippas and V. Maz'ya and A. Tertikas},
  journal= {arXiv preprint arXiv:math/0611484},
  year   = {2007}
}

Comments

22 pages

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