English

On improved fractional Sobolev-Poincar\'e inequalities

Classical Analysis and ODEs 2013-12-19 v1

Abstract

We prove a certain improved fractional Sobolev-Poincar\'e inequality on John domains; the proof is based on the equivalence of the corresponding weak and strong type inequalities. We also give necessary conditions for the validity of an improved fractional Sobolev-Poincar\'e inequality, in particular, we show that a domain having a finite measure and satisfying this inequality, and a `separation property', is a John domain.

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Cite

@article{arxiv.1312.5118,
  title  = {On improved fractional Sobolev-Poincar\'e inequalities},
  author = {Bartłomiej Dyda and Lizaveta Ihnatsyeva and Antti V. Vähäkangas},
  journal= {arXiv preprint arXiv:1312.5118},
  year   = {2013}
}

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