On the regularity of solutions to the Poisson equation in Musielak-Orlicz Spaces

  • Abdelmoujib Benkirane University Sidi Mohammed Ben Abdellah Faculty of Sciences Dhar El Mahraz Department of Mathematics Laboratory LAMA
  • Deval Sidi Mohamed University Sidi Mohammed Ben Abdellah Faculty of Sciences Dhar El Mahraz Department of Mathematics Laboratory LAMA
  • Mustafa Ait Khellou University Sidi Mohammed Ben Abdellah Faculty of Sciences Dhar El Mahraz Department of Mathematics Laboratory LAMA

Résumé

In this paper, we study some regularity results of solutions of the Poisson equation $\triangle u=f,$ in Musielak-Orlicz spaces.

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Bibliographies de l'auteur

Abdelmoujib Benkirane, University Sidi Mohammed Ben Abdellah Faculty of Sciences Dhar El Mahraz Department of Mathematics Laboratory LAMA
Laboratory LAMA, Department of Mathematics
Deval Sidi Mohamed, University Sidi Mohammed Ben Abdellah Faculty of Sciences Dhar El Mahraz Department of Mathematics Laboratory LAMA
Laboratory LAMA, Department of Mathematics
Mustafa Ait Khellou, University Sidi Mohammed Ben Abdellah Faculty of Sciences Dhar El Mahraz Department of Mathematics Laboratory LAMA
Laboratory LAMA, Department of Mathematics

Références

R. Adams, Sobolev spaces, Acad.press (1975).

M.L. Ahmed Oubeid, A.Benkirane and M. Sidi El vally, Strongly nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces, to appear in Bol. Soc. Parana. Mat.

E. Azroul, A. Benkirane, M. Tienari: On the regularity of solution to the poisson equation in Orlicz-spaces,Bull.Belg.Math.soc .(2000)

A. Benkirane, Potentiel de Riesz et problemes elliptiques dans les espaces d’Orlicz, these de Doctorat, Universit´e libre de Bruxelles,(1988).

A. Benkirane and J. P. Gossez, An approximation theorem in higher Orlicz-Sobolev spaces and application, Studia Math. 92(1989), pp. 231-255.

R. Dautray et J. L. Lions, Analyse Math´ematique et calcul numerique, volume 2, Masson (1987).

L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev Spaces With Variable Exponents, Lecture Notes in Mathematics (2017).

- Elias and M. Stein”Singular Integrals and Differentiability Properties of Functions” Princeton University press

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equation of second order, Springer Verlag (1983).

J. P. Gossez, Some appoximation properties in Orlicz-Sobolov spaces, studia Math. 74(1982) pp. 17-24.

J. P. gossez, Non linear elliptic boundary value problems for equation with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc. 190(1974) pp. 163-205.

Grter and Wildman, Manuscripa Math 37(1982), pp. 303-342.

M. Krasnosel’skii and Ya. Rutickii, Convex functions and Orlicz spaces, Noord-hoof, (1961).

A. Kufner, O. John and S. Fucik, Function spaces, Academia, (1977).

J. Musielak: Modular spaces and Orlicz spaces, Lecture Notes in Math. 1034, (1983).

M. Tienari, A degree theory for a class of mappings of monotone type in Orlicz-Sobolev spaces, Ann. acad. Scientiarum Fennice Helsinki(1994).

Publiée
2019-05-25
Rubrique
Research Articles