A Global Compactness type result for Palais–Smale sequences in fractional Sobolev spaces. (April 2015)

• Record Type: Journal Article
• Authors: Palatucci, Giampiero; Pisante, Adriano
• Is Part Of: Nonlinear analysis. Volume 117(2015)
• Page Start: 1
• Page End: 7
• Publication Date: 2015-04
• Subjects: primary 35J60 35C20 35B33 49J45; Profile decomposition -- Global compactness -- Fractional Sobolev -- Critical Sobolev exponent; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.12.027
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We extend the global compactness result by Struwe (1984) to any fractional Sobolev spaces H ̇ s ( Ω ), for 0 < s < N / 2 and Ω ⊂ R N a bounded domain with smooth boundary. The proof is a simple direct consequence of the so-called profile decomposition of Gérard (1998).