Description of the lack of compactness for the Sobolev imbedding

Gérard, P.. "Description of the lack of compactness for the Sobolev imbedding." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 213-233. <http://eudml.org/doc/197367>.

@article{Gérard2010,
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. },
author = {Gérard, P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Concentration-compactness; asymptotic analysis; Sobolev imbedding; almost orthogonality. ; Hilbert homogeneous Sobolev space; almost-orthogonal sum; superposition; sequences of translations and dilations; concentration-compactness principle},
language = {fre},
month = {3},
pages = {213-233},
publisher = {EDP Sciences},
title = {Description of the lack of compactness for the Sobolev imbedding},
url = {http://eudml.org/doc/197367},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Gérard, P.
TI - Description of the lack of compactness for the Sobolev imbedding
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 213
EP - 233
AB - 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.
LA - fre
KW - Concentration-compactness; asymptotic analysis; Sobolev imbedding; almost orthogonality. ; Hilbert homogeneous Sobolev space; almost-orthogonal sum; superposition; sequences of translations and dilations; concentration-compactness principle
UR - http://eudml.org/doc/197367
ER -