Blow-up analysis in dimension 2 and a sharp form of trudinger-moser inequality

Adimurthi, ; Druet, O. (2005) Blow-up analysis in dimension 2 and a sharp form of trudinger-moser inequality Communications in Partial Differential Equations, 29 (1 & 2). 295 - 322. ISSN 0360-5302

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Related URL: http://dx.doi.org/10.1081/PDE-120028854

Abstract

This paper deals with an improvement of the Trudinger-Moser inequality associated to the embedding of the standard Sobolev space H10(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 H10(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.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Ltd.
Keywords:Sobolev Spaces; Orlicz Space; Green's Function; Rescaling; Critical Growth
ID Code:11775
Deposited On:09 Nov 2010 09:25
Last Modified:10 May 2011 04:12

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