An approximation theorem in Musielak-Orlicz-Sobolev spaces

• Autorzy: Benkirane A. , Douieb J. , Ould Mohamedhen Val M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove the uniform boundedness of the operators of convolution in the Musielak-Orlicz spaces and the density of C[...]in the Musielak-Orlicz-Sobolev spaces by assuming a condition of Log-Hölder type of continuity.

Słowa kluczowe

EN

generalized Orlicz-Sobolev spaces; modular space; Musielak-Orlicz function; approximation theorem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2011
• Tom: Vol. 51, [Z] 1
• Strony: 109--120
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Benkirane A.

autor

Douieb J.

autor

Ould Mohamedhen Val M.

• Faculte des Sciences Dhar-Mahraz, Departement de Mathematiques B. P. 1796 Atlas Fes, Maroc,

Bibliografia

• [1] L. Aharouch, E. Azroul and M. Rhoudaf, Nonlinear Unilateral Problems in Orlicz spaces, Appl. Math., 200 (2006), 1-25.
• [2] L. Aharouch, A. Benkirane and M. Rhoudaf, Existence results for some unilateral problems without sign condition with obstacle free in Orlicz spaces, Nonlinear Anal. 68 (2008), no. 8, 2362-2380.
• [3] A. Benkirane, Approximations de type Hedberg dans les espaces WmLlog L(Ώ) et applications.(French) [Hedberg-type approximations in the spaces WmLlog L(Ώ) and applications], Ann. Fac. Sci. Toulouse Math. (5) 11 (1990), no. 2, 67-78.
• [4] A. Benkirane, A. Elmahi, An existence for a strongly nonlinear elliptic problem in Orlicz spaces, Nonlinear Analysis, 36 (1999) 11-24.
• [5] A. Benkirane, A. Emahi, A strongly nonlinear elliptic equation having natural growth terms and L1 data, Nonlinear Anal. 39 (2000), no. 4, Ser. A: Theory Methods, 403-411.
• [6] A. Benkirane, A. Emahi, D. Meskine, On the limit of some nonlinear elliptic problems, Arch. Inequal. Appl. 1 (2003), no. 2, 207-219.
• [7] A. Benkirane, J.P. Gossez, An approximation theorem in higher order Orlicz-Sobolev spaces and applications.Studia Math. 92 (1989), no. 3, 231-255.
• [8] A. Benkirane, M. Kbiri Alaoui, Sur certaines quations elliptiques non linarires a' second membre mesure. (French) [Certain nonlinear elliptic equations with right-hand-side measures], Forum Math. 12 (2000), no. 4, 385-395.
• [9] A. Benkirane, M. Mohamedhen Val, Some existance results for nonlinear elliptic equations in Musielak-Orlicz-Sobolev spaces, In preparation.
• [10] A. Elmahi, D. Meskine, Existence of solutions for elliptic equations having natural growth terms in orlicz spaces, Abstr. Appl. Anal. 12 (2004) 1031-1045.
• [11] A. Elmahi, D. Meskine, Non-linear elliptic problems having natural growth and L1 data in Orlicz spaces, Annali di Matematica (2004) 107-114.
• [12] A. Elmahi, D. Meskine, Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces, Nonlinear Analysis 60 (2005) 1-35.
• [13] J.P. Gossez, Nonlinear elliptic boundary value prolems for equations with rapidly (or slowly) increasing coefficients, Trans. Am. Malh. Soc. 190 (1974), 163-205.
• [14] J.P. Gossez, Some approximation properties in Orlicz-Sobolev spaces, Studia Math. 74 (1982), 17-24.
• [15] J.P. Gossez, V. Mustonen, Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal. 11 (1987), 379-392.
• [16] H. Hudzik, Density of C10 (Rn) in generalized Orlicz-Sobolev space WkM (Rn), Funct. Approximatio Comment. Math. 7 (1979), 15-21.
• [17] H. Hudzik, On generalized Orlicz-Sobolev space, Funct. Approximatio Comment. Math. 4 (1976), 37-51.
• [18] H. Hudzik, On problem of density of C10 () in generalized Orlicz-Sobolev space WkM (Ώ) for every open set Ώ Rn, Comment. Math. Parce Mat. 20 (1977), 65-78.
• [19] J. Musielak, Modular spaces and Orlicz spaces, Lecture Notes in Math. 1034 (1983).
• [20] M.M. Rao and Z.D. Ren, Theory of Orlicz spaces, Marcel Deker, New york, 1991.
• [21] S. G. SAMKO, Denseness of C∞ (Rn) in the generalized Sobolev spaces W1,p(x)(Rn), Intern. Soc. for Analysis, Applic. and Comput. 5 (2000), 333-342.