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sobolev imbedding

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Description of the lack of compactness for the Sobolev imbedding
P. Gérard
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 3 / 1998

Published online by Cambridge University Press:

15 August 2002, pp. 213-233

Print publication:

1998
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We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as analmost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of termsobtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the variousversions of the concentration-compactness principle.