A density problem for Sobolev spaces on Gromov hyperbolic domains. (May 2017)

• Record Type: Journal Article
• Authors: Koskela, Pekka; Rajala, Tapio; Zhang, Yi Ru-Ya
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 189
• Page End: 209
• Publication Date: 2017-05
• Subjects: 46E35; Sobolev space -- Density; 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.2016.07.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove that for a bounded domain Ω ⊂ R n which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when Ω is a finitely connected planar domain, the Sobolev space W 1, ∞ ( Ω ) is dense in W 1, p ( Ω ) for any 1 ≤ p < ∞ . Moreover if Ω is also Jordan or quasiconvex, then C ∞ ( R n ) is dense in W 1, p ( Ω ) for 1 ≤ p < ∞ .