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

Hajer Bahouri, Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

This paper is devoted to the description of the lack of compactness of H rad 1(R 2) 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
Volume260
Issue number1
DOIs
StatePublished - Jan 1 2011

Fingerprint

Sobolev Embedding
Orlicz Spaces
Compactness
Orlicz Norm
Lebesgue Space
Nonlinear Wave Equation
Exponential Growth

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

On the lack of compactness in the 2D critical Sobolev embedding. / Bahouri, Hajer; Majdoub, Mohamed; Masmoudi, Nader.

In: Journal of Functional Analysis, Vol. 260, No. 1, 01.01.2011, p. 208-252.

Research output: Contribution to journalArticle

Bahouri, Hajer ; Majdoub, Mohamed ; Masmoudi, Nader. / On the lack of compactness in the 2D critical Sobolev embedding. In: Journal of Functional Analysis. 2011 ; Vol. 260, No. 1. pp. 208-252.
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