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Concentration profiles for the Trudinger-Moser functional are shaped like toy pyramids
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 266, no 2, 676-692 p.Article in journal (Refereed) Published
Abstract [en]

This paper answers the conjecture of Adimurthi and Struwe [4], that the semilinear Trudinger-Moser functional J(u) = 1/2 integral(Omega) vertical bar del u vertical bar(2) dx - 1/8 pi integral(Omega) (e(4 pi u2) - 1) dx (0.1) (as well as functionals with more general critical nonlinearities) satisfies the Palais-Smale condition at all levels except n/2, n is an element of N. In this paper we construct critical sequences at any level c > 1/2. corresponding to a large family of distinct concentration profiles, indexed by closed subsets C of (0, 1), that arise in the two-dimensional case instead of the "standard bubble" in higher dimensions. The paper uses the notion of concentration of [2,5] developed in the spirit of Solimini [14] and of [15]. 

Place, publisher, year, edition, pages
2014. Vol. 266, no 2, 676-692 p.
Keyword [en]
Moser-Trudinger inequality, Elliptic problems in two dimensions, Concentration compactness, Global compactness, Profile decomposition, Weak convergence, Blowups, Palais-Smale sequences
National Category
URN: urn:nbn:se:uu:diva-216032DOI: 10.1016/j.jfa.2013.10.011ISI: 000328445700009OAI: oai:DiVA.org:uu-216032DiVA: diva2:689307
Available from: 2014-01-20 Created: 2014-01-17 Last updated: 2016-04-13

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