Defect of compactness in spaces of bounded variation
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
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  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.
Functions of bounded variation, 1-Laplacian, Concentration compactness, Subelliptic Sobolev spaces
IdentifiersURN: urn:nbn:se:uu:diva-298053DOI: 10.1016/j.jfa.2016.04.002ISI: 000376050400003OAI: oai:DiVA.org:uu-298053DiVA: diva2:946812