Poincar\'e inequalities in quasihyperbolic boundary condition domains
Classical Analysis and ODEs
2015-10-02 v5 Analysis of PDEs
Abstract
We study the validity of (q,p)-Poincar\'e inequalities, q<p, on domains in R^n which satisfy a quasihyperbolic boundary condition, i.e. domains whose quasihyperbolic metric satisfies a logarithmic growth condition. In the present paper, we show that the quasihyperbolic boundary condition domains support a (q,p)-Poincar\'e inequality whenever p>p_0, where p_0 is an explicit constant depending on q, on the logarithmic growth condition, and on the boundary of the domain.
Keywords
Cite
@article{arxiv.1201.5789,
title = {Poincar\'e inequalities in quasihyperbolic boundary condition domains},
author = {Ritva Hurri-Syrjänen and Niko Marola and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:1201.5789},
year = {2015}
}