# Description of the lack of compactness for the Sobolev imbedding

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 3, page 213-233
- ISSN: 1292-8119

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topGérard, 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 -

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