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arXiv · 1312.5118

On improved fractional Sobolev-Poincaré inequalities

Bartłomiej Dyda·Lizaveta Ihnatsyeva·Antti V. Vähäkangas
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Abstract

We prove a certain improved fractional Sobolev-Poincaré 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-Poincaré 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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Bartłomiej Dyda, Lizaveta Ihnatsyeva, Antti V. Vähäkangas. 2013-12-18. On improved fractional Sobolev-Poincaré inequalities. https://arxiv.org/abs/1312.5118

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