Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
2007 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 332, no 1, 190-208 p.Article in journal (Refereed) Published
In the setting of metric measure spaces equipped with a doubling measure supporting a weak p-Poincaré inequality with 1 ≤ p < ∞, we show that any uniform domain Ω is an extension domain for the Newtonian space N1, p (Ω) and that Ω, together with the metric and the measure inherited from X, supports a weak p-Poincaré inequality. For p > 1, we obtain a near characterization of N1, p-extension domains with local estimates for the extension operator. © 2006 Elsevier Inc. All rights reserved.
Place, publisher, year, edition, pages
2007. Vol. 332, no 1, 190-208 p.
IdentifiersURN: urn:nbn:se:liu:diva-36130DOI: 10.1016/j.jmaa.2006.09.064Local ID: 30029OAI: oai:DiVA.org:liu-36130DiVA: diva2:256978