Defect of compactness in spaces of bounded variation

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 (xk)k∈N⊂X is a sequence (Sk)k∈N, such that (xk−Sk)k∈N is a convergent sequence in Y, and, furthermore, Sk has the particular form Sk=∑n∈Ngk(n)w(n) with gk(n)∈D and w(n)∈X. This paper extends the profile decomposition proved by Solimini [10] for Sobolev spaces H˙1,p(RN) with 1