Open Access
Fall 2012 On the $(1,p)$-Poincaré inequality
Petteri Harjulehto, Ritva Hurri-Syrjänen, Antti V. Vähäkangas
Illinois J. Math. 56(3): 905-930 (Fall 2012). DOI: 10.1215/ijm/1391178555


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, $1\le q\le p$.


Download Citation

Petteri Harjulehto. Ritva Hurri-Syrjänen. Antti V. Vähäkangas. "On the $(1,p)$-Poincaré inequality." Illinois J. Math. 56 (3) 905 - 930, Fall 2012.


Published: Fall 2012
First available in Project Euclid: 31 January 2014

zbMATH: 1287.46029
MathSciNet: MR3161358
Digital Object Identifier: 10.1215/ijm/1391178555

Primary: 46E35
Secondary: 26D10

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 3 • Fall 2012
Back to Top