A density problem for Sobolev spaces on Gromov hyperbolic domains. (May 2017) - Koskela, Pekka; Rajala, Tapio; Zhang, Yi Ru-Ya
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 < ∞ .