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Approximation by functions in C0∞(Ω) in Orlicz - Sobolev spaces

Liskowski M.

Fasciculi Mathematici

2005

Nr 36

73-82

The results presented in this paper concern the identity of spaces Wk, M Ω and Wk, M Ω generated by &phi-functions M with parameter for some class domains Ω ⊂ Rn and they are the extension of analogous results for clasical Sobolev spaces. The problem of approximation of elements in Wk, M Ω by smooth functions on various domains Ω ⊂ Rn were investigated by different authors for classic Sobolev spaces with integer values of k as well as for some generalization of Sobolev space to the case of noninteger values k (see e.g. N. Meyers and J. Serrin [11] in the case M(u) =up, p> 1; T. K. Donaldson and N. S. Trudinger [2], when M is arbitrary N-function; H. Hudzik [3], [4], [5], [6]. [7], when M is TV-function which depends on parameter; M. Liskowski [9] [10] for some family of generalized Orlicz-Sobolev space, when k is noninteger and M is N-function with parameter).