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Description of the lack of compactness for the Sobolev imbedding

Published online by Cambridge University Press:  15 August 2002

P. Gérard
P. Gérard*
Affiliation:
(Patrick.Gerard@math.u-psud.fr)
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Abstract

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.

Keywords

Concentration-compactnessasymptotic analysisSobolev imbeddingalmost orthogonality.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 3 , 1998 , pp. 213 - 233
Copyright
© EDP Sciences, SMAI, 1998

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