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Essential norms and localization moduli of Sobolev embeddings for general domains
Department of Mathematics Ohio State University.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2008 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 78, no 2, 373-391 p.Article in journal (Refereed) Published
Abstract [en]

We introduce new measures of non-compactness for the embedding operator Ep,q(Ω):Lp1(Ω)→Lq(Ω) and describe their relations with the essential norm of Ep, q(Ω), 'local' isoperimetric and isocapacitary constants. An explicit formula for the essential norm of Ep, q(Ω) is obtained for domains with a power cusp on the boundary and bounded C1 domains. The Neumann problem for a particular Schrödinger operator is discussed on domains with a power cusp.

Place, publisher, year, edition, pages
2008. Vol. 78, no 2, 373-391 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-43167DOI: 10.1112/jlms/jdn035Local ID: 72249OAI: oai:DiVA.org:liu-43167DiVA: diva2:264026
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2010-06-10

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Maz´ya, Vladimir

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