T. Kilpel\"ainen
Smooth approximation in weighted Sobolev spaces

Comment.Math.Univ.Carolinae 38,1 (1997) 29-35.

Abstract:We give necessary and sufficient conditions for the equality $H=W$ in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.

Keywords: weighted Sobolev spaces, Poincar\'e inequality
AMS Subject Classification: 46E35