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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