On the lack of compactness in the 2D critical Sobolev embedding

Hajer Bahouri, Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review


This paper is devoted to the description of the lack of compactness of Hrad1(R2) in the Orlicz space. Our result is expressed in terms of the concentration-type examples derived by P.-L. Lions (1985) in [24]. The approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of Sobolev embedding in Lebesgue spaces and takes into account the variational aspect of Orlicz spaces. We also investigate the feature of the solutions of nonlinear wave equation with exponential growth, where the Orlicz norm plays a decisive role.

Original languageEnglish (US)
Pages (from-to)208-252
Number of pages45
JournalJournal of Functional Analysis
Issue number1
StatePublished - Jan 1 2011


  • Lack of compactness
  • Nonlinear wave equation
  • Orlicz space
  • Sobolev critical exponent
  • Strichartz estimates
  • Trudinger-Moser inequality

ASJC Scopus subject areas

  • Analysis


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