Density of smooth functions in Sobolev spaces "wth mixed functions"

• Autorzy: Liskowski M.
• Języki publikacji: EN

Abstrakty

EN

The results presented in this paper concern approximation by smooth functions in the Sobolev spaces defined by means of a modular (1). These spaces can be a natural medium to study the partial differential equations with rapidly or slowly increasing coefficients (i.e. the coefficients are of a nonpolynomial type).

Słowa kluczowe

EN

modular space; Sobolev space

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 53
• Strony: 77--83
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Liskowski M.

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

Bibliografia

• [1] Hudzik H., Musielak J., Urbański R., Linear operators in modular spaces. An application to approximation theory, Proc. Conference of Approximation and Function Spaces, (Gdańsk, 1979), (1981), 279-286.
• [2] Liskowski M., Sobolev spaces ”with mixed functions”, Fasc. Math., 42 (2012), 73-82.
• [3] Liskowski M., On approximation by means of linear operators in generalized Orlicz spaces, Int. Journal of Pure and Applied Mathematics, 37(2)(2007), 165-180.
• [4] Musielak J., On approximation of functions of two variables by integral means and their generalization, Atti Sem. Mat. Univ. Modena, XLVI(1998), 335-349.
• [5] Musielak J., Orlicz Spaces and Modular Spaces, Lecture Notes in Math., 1034, Springer-Verlag (1983).