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Defect of compactness in spaces of bounded variation
TIFR CAM, PB 6503, Bangalore 560065, Karnataka, India.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
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]

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.

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

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