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

Hajer Bahouri; Mohamed Majdoub; Nader Masmoudi

doi:10.1016/j.jfa.2010.08.016

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

Hajer Bahouri, Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to the description of the lack of compactness of H_rad¹(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 language	English (US)
Pages (from-to)	208-252
Number of pages	45
Journal	Journal of Functional Analysis
Volume	260
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2010.08.016
State	Published - Jan 1 2011

Keywords

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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10.1016/j.jfa.2010.08.016

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KW - Strichartz estimates

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

Abstract

Keywords

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