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

• Autorzy: Liskowski M.
• Języki publikacji: EN

Abstrakty

EN

The results presented in this paper concern the identity of spaces W^{k, M} Ω and W^{k, 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 W^{k, 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) =u^p, 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).

Słowa kluczowe

EN

Orlicz-Sobolev space; dual of Orlicz-Sobolev space; approximation by smooth function; generalized Sobolev space; polar set

PL

przestrzeń Orlicza-Soboleva; aproksymacja

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 36
• Strony: 73--82
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Liskowski M.

• Institute of Mathematics, Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland,

Bibliografia

• [1] Adams R.A., Sobolev spaces, Academic Press, New York - San Francisco -London 1975.
• [2] Donaldson T.K., Trudinger N.S., Orlicz-Sobolev spaces and imbedding theorems, J. Functional Analysis, 8(1971), 52-75.
• [3] Hudzik H., On density of C0∞(Ω) in Orlicz-Sobolev space WkM(Ω) for every open set Ω c Rn , Funct, et Approximatio, 5(1977), 113-128.
• [4] Hudzik H., On problem of density of in generalized Orlicz-Sobolev space WkM(Ω) for every open set Ω c Rn , Comm. Mathematicae, 20(1977), 5-78.
• [5] Hudzik H., On continuity of the imbedding operation from WkM(Ω) into WkM2(Ω), Funct, et Approximatio, 6(1978), 111-118.
• [6] Hudzik H., Density of C0∞(Ω) in generalized Orlicz-Sobolev space WkM(Ω), Funct. et Approximatio, 7(1979), 15-21.
• [7] Hudzik H., The problems of separability, duality, reflexivity and of comparison for generalized Orlicz-Sobolev spaces WkM(Ω), Comm. Mathematicae, 21(1979), 315-324.
• [8] Kozek A. Convex integral functionals in Orlicz spaces. Comm. Mathematicae, 21(1979), 109-135.
• [9] Liskowski M., Density of C0∞(Rn) generalized Besov space Bk,ɸ(Rn) Funct. et Approximatio, 15(1986), 185-193.
• [10] Liskowski M., Approximation in Orlicz-Slobodecki space by functions in C∞(Ω), Fasciculi Mathematici, 29(1999), 43-54.
• [11] Meyers N., Serrin J., H = W, Proc. Nat. Acad. Sci., USA, 51(1964), 1055-1056.
• [12] Musielak J., Orlicz spaces and modular spaces. Lecture Notes in Math. 1034, Springer, 1983.