Poincare inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces

摘要

In the setting of metric measure spaces equipped with a doubling measure supporting a weak p-Poincare inequality with 1 <= p < infinity, we show that any uniform domain Omega is an extension domain for the Newtonian space N-1,N-P(Omega) and that Omega, together with the metric and the measure inherited from X, supports a weak p-Poincare inequality. For p > 1, we obtain a near characterization of N-1,N-P-extension domains with local estimates for the extension operator. (c) 2006 Elsevier Inc. All rights reserved.