Abstract
We show that $s$-John domains satisfy the $(1,p)$-Poincaré inequality for all finite $p>p_{0}$. We prove that the lower bound $p_{0}$ is sharp. We formulate a conjecture concerning $(q,p)$-Poincaré inequalities in $s$-John domains, $1\le q\le p$.
Citation
Petteri Harjulehto. Ritva Hurri-Syrjänen. Antti V. Vähäkangas. "On the $(1,p)$-Poincaré inequality." Illinois J. Math. 56 (3) 905 - 930, Fall 2012. https://doi.org/10.1215/ijm/1391178555
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