2012/11/16 by Cyril Tintarev, Tintarev, Cyril, David G. Costa +1 · 1 citation
Chemistry · Computer Science · Engineering · Mathematics · #35J20 #35J35 #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Diffusion Coefficients in Liquids #FOS: Mathematics #Graph theory and applications #Markov Chains and Monte Carlo Methods #Nonlinear Partial Differential Equations #Phase Equilibria and Thermodynamics #math.AP #msc:35J20 #msc:35J35 #msc:35J60
paper · pdf · doi:10.48550/arxiv.1211.3835
arxiv created 2012/11/16 · openalex publication_date 2012/11/16 · arxiv updated 2012/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper answers the conjecture of Adimurthi and Struwe that the semilinear Trudinger-Moser functional (as well as functionals with more general critical nonlinearities) satisfies the Palais-Smale condition at all levels except n/2 for integer n. In this paper we construct critical sequences at any level greater than 1/2 corresponding to a large family of distinct concentration profiles, indexed by all closed subsets C of (0,1) that arise in the two-dimensional case instead of the "standard bubble" in higher dimensions. The approach is based on the profile decomposition in the style of Solimini.