Denseness of C 0 ∞(R N ) in the Generalized Sobolev Spaces

By S. Samko. 2000

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Variable exponent Sobolev spaces on metric measure spaces (2006, background): “Variable exponent spaces have been independently discovered by several investigators [9, 21, 28, 30] and are related to differential equations with non-standard coercivity conditions.”
Quasilinear elliptic problems with nonstandard growth. (2011, background): “Samko [16, 17, 18] working based on earlier Russian work (Sharapudinov [19] and Zhikov [20]), Fan and collaborators [5, 6, 7, 8] drawing inspiration from the study of differential equations(e.”
Hardy's Inequality in a Variable Exponent Sobolev Space (2005, background): “For instance, if p is bounded and log-Hölder continuous in R, then C∞ 0 (R) is dense in W 1,p(·)(Rn), [22].”
Operators of harmonic analysis in weighted spaces with non-standard growth (2008, unknown): “…and C.J.Neugebauer [11], L. Diening [13], [14], [15], L.Diening and M.Ruˇ z iˇ c ka [17], V. Kokilashvili, N.Samko and S.Samko [38], V.Kokilashvili and S.Samko [45], [41], [42], [43], A.Nekvinda [59], S.Samko [71], [72], [73], S.Samko, E.Shargorodsky and B.Vakulov [75] and references therein.”