Calculus of Variations and Geometric Measure Theory

R. Hurri-Syrjänen - N. Marola - A. V. Vähäkangas

Poincare inequalities in quasihyperbolic boundary condition domains

created by marola on 27 Jan 2012
modified on 18 Jul 2015


Published Paper

Inserted: 27 jan 2012
Last Updated: 18 jul 2015

Journal: Manuscripta Math.
Year: 2015


We study the validity of (q,p)-Poincare inequalities, q<p, on domains in ’Rn which satisfy a quasihyperbolic boundary condition, i.e. domains whose quasihyperbolic metric satisfi es a logarithmic growth condition. In the present paper, we show that the quasihyperbolic boundary condition domains support a (q,p)-Poincare inequality whenever p>p0, where p0 is an explicit constant depending on q, on the logarithmic growth condition, and on the boundary of the domain.