On the regularity of solutions to the Poisson equation in Musielak-Orlicz Spaces
DOI:
https://doi.org/10.5269/bspm.v38i6.36696Keywords:
Musielak-Orlicz spaces, Distributions, Poisson equation, Newtonian potentialAbstract
In this paper, we study some regularity results of solutions of the Poisson equation $\triangle u=f,$ in Musielak-Orlicz spaces.References
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2. 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.
3. E. Azroul, A. Benkirane, M. Tienari: On the regularity of solution to the poisson equation in Orlicz-spaces,Bull.Belg.Math.soc .(2000)
4. A. Benkirane, Potentiel de Riesz et problemes elliptiques dans les espaces d’Orlicz, these de Doctorat, Universit´e libre de Bruxelles,(1988).
5. A. Benkirane and J. P. Gossez, An approximation theorem in higher Orlicz-Sobolev spaces and application, Studia Math. 92(1989), pp. 231-255.
6. R. Dautray et J. L. Lions, Analyse Math´ematique et calcul numerique, volume 2, Masson (1987).
7. L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev Spaces With Variable Exponents, Lecture Notes in Mathematics (2017).
8. - Elias and M. Stein”Singular Integrals and Differentiability Properties of Functions” Princeton University press
9. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equation of second order, Springer Verlag (1983).
10. J. P. Gossez, Some appoximation properties in Orlicz-Sobolov spaces, studia Math. 74(1982) pp. 17-24.
11. 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.
12. Grter and Wildman, Manuscripa Math 37(1982), pp. 303-342.
13. M. Krasnosel’skii and Ya. Rutickii, Convex functions and Orlicz spaces, Noord-hoof, (1961).
14. A. Kufner, O. John and S. Fucik, Function spaces, Academia, (1977).
15. J. Musielak: Modular spaces and Orlicz spaces, Lecture Notes in Math. 1034, (1983).
16. M. Tienari, A degree theory for a class of mappings of monotone type in Orlicz-Sobolev spaces, Ann. acad. Scientiarum Fennice Helsinki(1994).
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2019-05-25
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