Lack of compactness in the 2D critical Sobolev embedding, the general case

Hajer Bahouri, Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

This Note is devoted to the description of the lack of compactness of the Sobolev embedding of H1(R2) in the critical Orlicz space L(R2). It turns out that up to cores our result is expressed in terms of the concentration-type examples derived by J. Moser (1971) in [16] as in the radial setting investigated in Bahouri et al. (2011) [5]. However, the analysis we used in this work is strikingly different from the one conducted in the radial case which is based on an L estimate far away from the origin and which is no longer valid in the general frame work. The strategy we adopted to build the profile decomposition in terms of examples by Moser concentrated around cores is based on capacity arguments and relies on an extraction process of mass concentrations.

Original languageEnglish (US)
Pages (from-to)177-181
Number of pages5
JournalComptes Rendus Mathematique
Volume350
Issue number3-4
DOIs
StatePublished - Feb 2012

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Sobolev Embedding
Compactness
Orlicz Spaces
Valid
Decompose
Estimate
Strategy
Profile
Framework

ASJC Scopus subject areas

  • Mathematics(all)

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Lack of compactness in the 2D critical Sobolev embedding, the general case. / Bahouri, Hajer; Majdoub, Mohamed; Masmoudi, Nader.

In: Comptes Rendus Mathematique, Vol. 350, No. 3-4, 02.2012, p. 177-181.

Research output: Contribution to journalArticle

Bahouri, Hajer ; Majdoub, Mohamed ; Masmoudi, Nader. / Lack of compactness in the 2D critical Sobolev embedding, the general case. In: Comptes Rendus Mathematique. 2012 ; Vol. 350, No. 3-4. pp. 177-181.
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