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Blow-up Analysis in Dimension 2 and a Sharp Form and a Sharp Form of Trudinger-Moser Inequality.
- Source :
-
Communications in Partial Differential Equations . Jan/Feb2004, Vol. 29 Issue 1/2, p295-322. 28p. - Publication Year :
- 2004
-
Abstract
- This paper deals with an improvement of the Trudinger-Moser inequality associated to the embedding of the standard Sobolev space H0¹(Ω) into Orlicz spaces for Ω a smooth bounded domain in R². The inequality proved here gives in particular precise informations on a previous result obtained by Lions and can be very useful in the study of lack of compactness of the embedding of H0¹(Ω) into {exp(4πu²) ∈ L¹(Ω)}. We also provide a general asymptotic analysis for sequences of solutions to elliptic PDE's with critical Sobolev growth which blow up at some point. We obtain in particular a result which is well-known in higher dimensions: the concentration points are located at critical points of the regular part of the Green function of the linear operator involved in the equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03605302
- Volume :
- 29
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Communications in Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 12735657