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On a version of Trudinger-Moser inequality with Möbius shift invariance
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 39, no 1-2, 203-212 p.Article in journal (Refereed) Published
Abstract [en]

The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of the Trudinger-Moser inequality on the open unit disk B subset of R-2, recently proved by Mancini and Sandeep [g], (Arxiv 0910.0971). Unlike the original Trudinger-Moser inequality, this inequality is invariant with respect to the Mobius automorphisms of the unit disk, and as such is a closer analogy of the critical nonlinearity integral |u|(2)* in the higher dimension than the original Trudinger-Moser nonlinearity.

Place, publisher, year, edition, pages
2010. Vol. 39, no 1-2, 203-212 p.
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URN: urn:nbn:se:uu:diva-135840DOI: 10.1007/s00526-010-0307-5ISI: 000279580600009OAI: oai:DiVA.org:uu-135840DiVA: diva2:375718
Available from: 2010-12-08 Created: 2010-12-08 Last updated: 2011-03-01Bibliographically approved

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