Geodesic
Smooth approximation in weighted Sobolev spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 29-35

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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.
Classification : 41A65, 46E35
Keywords: weighted Sobolev spaces; Poincaré inequality 
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     author = {Kilpel\"ainen, T.},
     title = {Smooth approximation in weighted {Sobolev} spaces},
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     pages = {29--35},
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     volume = {38},
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     zbl = {0886.46035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1997__38_1_a2/}
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Kilpeläinen, T. Smooth approximation in weighted Sobolev spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 29-35. http://geodesic.mathdoc.fr/item/CMUC_1997__38_1_a2/