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Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-1238-6751
Department of Mathematical Sciences University of Cincinnnati.
2007 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 332, no 1, 190-208 p.Article in journal (Refereed) Published
Abstract [en]

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.
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URN: urn:nbn:se:liu:diva-36130DOI: 10.1016/j.jmaa.2006.09.064Local ID: 30029OAI: diva2:256978
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-05-04

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Björn, Jana
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