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Type: Artigo de periódico
Title: On an inequality by N. Trudinger and J. Moser and related elliptic equations
Author: de Figueiredo, DG
Do O, JM
Ruf, B
Abstract: It has been shown by Trudinger and Moser that for normalized functions u of the Sobolev space W-1,W-N (Omega), where Omega is a bounded domain in R-N, one has integral (Omega) exp(alpha (N)\u\(N/(N-1)))dx less than or equal to C-N, where alpha (N) is an explicit constant depending only on N, and C-N is a constant depending only on N and Omega. Carleson and Chang proved that there exists a corresponding extremal function in the case that Omega is the unit ball in R-N. In this paper we give a new proof, a generalization, and a new interpretation of this result. In particular, we give an explicit sequence that is maximizing for the above integral among all normalized "concentrating sequences." As an application, the existence of a nontrivial solution for a related elliptic equation with "Trudinger-Moser" growth is proved. (C) 2002 John Wiley & Sons, Inc.
Country: EUA
Editor: John Wiley & Sons Inc
Citation: Communications On Pure And Applied Mathematics. John Wiley & Sons Inc, v. 55, n. 2, n. 135, n. 152, 2002.
Rights: fechado
Identifier DOI: 10.1002/cpa.10015
Date Issue: 2002
Appears in Collections:Unicamp - Artigos e Outros Documentos

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