Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality

We prove a concentration-compactness principle for the Trudinger-Moser functional associated with a class of weighted Sobolev spaces including fractional dimensions. Based in this result and using blow up analysis we establish a sharp form of Trudinger-Moser type inequality for this class of weighte...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 52; no. 1-2; pp. 125 - 163
Main Authors de Oliveira, José Francisco, do Ó, João Marcos
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2015
Springer Nature B.V
Subjects
Analysis
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Control
Inequalities
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Partial differential equations
Sobolev space
Systems Theory
Theoretical
26D10
46E35
35B33
Online AccessGet full text
ISSN0944-2669
1432-0835
DOI10.1007/s00526-014-0707-z

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Summary:We prove a concentration-compactness principle for the Trudinger-Moser functional associated with a class of weighted Sobolev spaces including fractional dimensions. Based in this result and using blow up analysis we establish a sharp form of Trudinger-Moser type inequality for this class of weighted Sobolev spaces. Moreover, we discuss the existence of extremal for the maximizing problem associated with this new Trudinger-Moser inequality.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-014-0707-z