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Defect of compactness in spaces of bounded variationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 271, no 1, 37-48 p.Article in journal (Refereed) PublishedText
##### Abstract [en]

##### Place, publisher, year, edition, pages

2016. Vol. 271, no 1, 37-48 p.
##### Keyword [en]

Functions of bounded variation, 1-Laplacian, Concentration compactness, Subelliptic Sobolev spaces
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-298053DOI: 10.1016/j.jfa.2016.04.002ISI: 000376050400003OAI: oai:DiVA.org:uu-298053DiVA: diva2:946812
#####

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##### Funder

Wenner-Gren Foundations
Available from: 2016-07-06 Created: 2016-06-29 Last updated: 2016-07-06Bibliographically approved

Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. Let X be a Banach space continuously imbedded into a Banach space Y, and let D be a group of linear isometric operators on X. A profile decomposition in X, relative to D and Y, for a bounded sequence (x(k))(k is an element of N) subset of X is a sequence (S-k)(k is an element of N), such that (x(k) - S-k)(k is an element of N) is a convergent sequence in Y, and, furthermore, S-k has the particular form S-k = Sigma(n is an element of N)g(k)((n))W((n)) with g(k)((n)) is an element of D and w((n)) is an element of X. This paper extends the profile decomposition proved by Solimini [10] for Sobolev spaces (H) over dot(1,P)(R-N) with 1 < p < N to the non-reflexive case p = 1. Since existence of "concentration profiles" w((n)) relies on weak-star compactness, and the space (H) over dot(1,1) is not a conjugate of a Banach space, we prove a corresponding result for a larger space of functions of bounded variation. The result extends also to spaces of bounded variation on Lie groups.

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