Gérard, P. Description of the lack of compactness for the Sobolev imbedding. (French) Zbl 0907.46027 ESAIM, Control Optim. Calc. Var. 3, 213-233 (1998). Summary: We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as an almost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of terms obtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the various versions of the concentration-compactness principle. Cited in 7 ReviewsCited in 74 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 49K10 Optimality conditions for free problems in two or more independent variables Keywords:Hilbert homogeneous Sobolev space; almost-orthogonal sum; superposition; sequences of translations and dilations; concentration-compactness principle PDFBibTeX XMLCite \textit{P. Gérard}, ESAIM, Control Optim. Calc. Var. 3, 213--233 (1998; Zbl 0907.46027) Full Text: DOI EuDML