Existence of solutions for unilateral problems with L¹ data in Orlicz spaces
DOI:
https://doi.org/10.4067/S0716-09172004000300007Keywords:
Orlicz Sobolev spaces, boundary value problems, truncations, unilateral problems, espacios de Orlicz Sobolev, problemas de valor de acotamiento, truncaciones, problemas unilaterales.Abstract
This article is concerned with the existence result of the unilateral problem associated to equations of the typeAu + g(x, u, ?u) = f,
in Orlicz spaces, where f ? L¹(?), the term g is a nonlinearity having natural growth and satisfying the sign condition. Some stability and positivity properties of solutions are proved.
References
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[7] A. Benkirane and J. P. Gossez, An approximation theorem for higher order Orlicz-Sobolev spaces, Studia Math., 92, pp. 231-255, (1989).
[8] G. Dalmaso, F. Murat, L. Orsina and A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup Pisa, Cl. Sci. 12, 4, pp. 741-808, (1997).
[9] A. Elmahi, D. Meskine, Unilateral elliptic problems in L1 with natural growth terms, To appear Nonlinear and convex analysis.
[10] M. Fuchs and L. Gongbao, L?-bounds for elliptic equations on Orlicz-Sobolev spaces, Archiv der Mathematik, 72, pp. 293-297, (1999).
[11] M. Fuchs and G. Seregin, Variational methods for fluids for PrandtlEyring type and plastic materials with logarithmic hardening, Preprint No. 476. SFB256, Universität Bonn, Math. Methods Appl. Sci. in press.
[12] M. Fuchs and G. Seregin, A regurality theory for variational integrals with LlnL-growth, Calc. of Variations , 6, pp. 171-187, (1998).
[13] M. Fuchs and G. Seregin, Regurality for solutions of variational problems in the deformation theory of plasticity with logarithmic hardening, Preprint No. 421, SFB256, Universität Bonn.
[14] J. P. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc., 190, pp. 163-205, (1974).
[15] J. P. Gossez and V. Mustonen, Variational inequalities in OrliczSobolev spaces, Nonlinear Anal. 11, pp. 379-392, (1987).
[16] M. A. Krasnoselskii and Y. B. Rutikii , Convex functions and Orlicz spaces, Noordhoff Groningen, (1969).
[17] A. Porretta, Existence for elliptic equations in L1 having lower order terms with natural growth, Portugal. Math. 57, pp. 179-190, (2000).
[2] P. Bénilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre and J. L. Vazquez, An L1-theory of existence and uniqueness of nonlinear elliptic equations., Ann. Scuola Norm. Sup. Pisa 22, pp. 240-273, (1995).
[3] A. Benkirane , Approximation de type de Hedberg dans les espaces WmLlogL(?) et application, Ann. Fac. Sci. Toulouse. 11, 4 , pp. 67-78, (1990).
[4] A. Benkirane and A. Elmahi, An existence theorem for a strongly nonlinear elliptic problems in Orlicz spaces, Nonlinear Anal. T. M. A., 36, pp. 11-24, (1999).
[5] A. Benkirane and A. Elmahi, A strongly nonlinear elliptic equation having natural growth terms and L1 data, Nonlinear Anal. T. M. A., 39, pp. 403-411, (2000).
[6] A. Benkirane, A. Elmahi, and D. Meskine , An existence theorem for a class of elliptic problems in L1, Applicationes Mathematicae., 29, 4 , pp. 439-457, (2002).
[7] A. Benkirane and J. P. Gossez, An approximation theorem for higher order Orlicz-Sobolev spaces, Studia Math., 92, pp. 231-255, (1989).
[8] G. Dalmaso, F. Murat, L. Orsina and A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup Pisa, Cl. Sci. 12, 4, pp. 741-808, (1997).
[9] A. Elmahi, D. Meskine, Unilateral elliptic problems in L1 with natural growth terms, To appear Nonlinear and convex analysis.
[10] M. Fuchs and L. Gongbao, L?-bounds for elliptic equations on Orlicz-Sobolev spaces, Archiv der Mathematik, 72, pp. 293-297, (1999).
[11] M. Fuchs and G. Seregin, Variational methods for fluids for PrandtlEyring type and plastic materials with logarithmic hardening, Preprint No. 476. SFB256, Universität Bonn, Math. Methods Appl. Sci. in press.
[12] M. Fuchs and G. Seregin, A regurality theory for variational integrals with LlnL-growth, Calc. of Variations , 6, pp. 171-187, (1998).
[13] M. Fuchs and G. Seregin, Regurality for solutions of variational problems in the deformation theory of plasticity with logarithmic hardening, Preprint No. 421, SFB256, Universität Bonn.
[14] J. P. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc., 190, pp. 163-205, (1974).
[15] J. P. Gossez and V. Mustonen, Variational inequalities in OrliczSobolev spaces, Nonlinear Anal. 11, pp. 379-392, (1987).
[16] M. A. Krasnoselskii and Y. B. Rutikii , Convex functions and Orlicz spaces, Noordhoff Groningen, (1969).
[17] A. Porretta, Existence for elliptic equations in L1 having lower order terms with natural growth, Portugal. Math. 57, pp. 179-190, (2000).
Published
2017-05-22
How to Cite
[1]
L. Aharouch and M. Rhoudaf, “Existence of solutions for unilateral problems with L¹ data in Orlicz spaces”, Proyecciones (Antofagasta, On line), vol. 23, no. 3, pp. 293-317, May 2017.
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