Existence of solutions of degenerated unilateral problems with $L^1$ data

Lahsen Aharouch; Youssef Akdim

doi:10.5802/ambp.185

Existence of solutions of degenerated unilateral problems with

L^{1}

data

Lahsen Aharouch ¹; Youssef Akdim ¹

¹ Faculté des Sciences Dhar-Mahraz Dép. de Math. et Informatique B.P 1796 Atlas Fès. Fès MAROC

Annales mathématiques Blaise Pascal, Volume 11 (2004) no. 1, pp. 47-66.

Abstract
Résumé

In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type $A u + g (x, u, \nabla u) = f - div F,$ where $A$ is a Leray-Lions operator and $g$ is a Carathéodory function having natural growth with respect to $| \nabla u |$ and satisfying the sign condition. The second term is such that, $f \in L^{1} (Ω)$ and $F \in Π_{i = 1}^{N} L^{p^{'}} (Ω, w_{i}^{1 - p^{'}})$ .

MR: 2077238 | Zbl: 02207858

DOI: 10.5802/ambp.185

Author's affiliations:

Lahsen Aharouch ¹; Youssef Akdim ¹

¹ Faculté des Sciences Dhar-Mahraz Dép. de Math. et Informatique B.P 1796 Atlas Fès. Fès MAROC

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Lahsen Aharouch; Youssef Akdim. Existence of solutions of degenerated unilateral problems with $L^1$ data. Annales mathématiques Blaise Pascal, Volume 11 (2004) no. 1, pp. 47-66. doi : 10.5802/ambp.185. https://ambp.centre-mersenne.org/articles/10.5802/ambp.185/

References
Cited by

[1] Y. Akdim; E. Azroul; A. Benkirane Existence of solutions for quasilinear degenerated elliptic equations, Electronic J. Diff. Eqns., Volume 2001 (2001) no. 71, pp. 1-19 | MR | Zbl

[2] Y. Akdim; E. Azroul; A. Benkirane Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems, Annale Mathématique Blaise Pascal, Volume 10 (2003), pp. 1-20 | DOI | Numdam | MR | Zbl

[3] E. Azroul; A. Benkirane; O. Filali Strongly nonlinear degenerated unilateral problems with $L^{1}$ data, Electronic J. Diff. Eqns. (Conf. 09. 2002), pp. 46-64 | Zbl

[4] P. Bénilan; L. Boccardo; T. Gallouët; R. Gariepy; M. Pierre; J. L. Vazquez An $L^{1}$ -theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa, Volume 22 (1995), pp. 240-273 | Numdam | MR

[5] L. Boccardo; T. Gallouët Non-linear Elliptic Equations with right hand side Measures, commun. In partial Differential Equations, Volume 17 (1992), pp. 641-655 | MR | Zbl

[6] L. Boccardo; T. Gallouët Strongly non-linear Elliptic Equations having natural growth and $L^{1}$ data, Nonlinear Anal., Volume 19 (1992), pp. 573-578 | DOI | MR | Zbl

[7] L. Boccardo; T. Gallouët; F. Murat A unified presentation of tow existence results for problems with natural growth, in : Progress in Partial Differential Equations : The Metz Surveys 2, M. Chipot (ed), Pitman Res. Notes Math. Ser. 296, Longman (1993), pp. 127-137 | MR | Zbl

[8] L. Boccardo; F. Murat; J.-P. Puel Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Math. Pura Appl., Volume 152 (1988), pp. 183-196 | DOI | MR | Zbl

[9] G. Dalmaso; F. Murat; L. Orsina; A. Prignet Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup Pisa Cl. Sci, Volume 12 (1999) no. 4, pp. 741-808 | Numdam | MR | Zbl

[10] P. Drabek; A. Kufner; F. Nicolosi Nonlinear elliptic equations, singular and degenerate cases, University of West Bohemia, 1996

[11] A. Elmahi; D. Meskine Unilateral elleptic problems in $L^{1}$ with natural growth terms (To appear Nonlinear and convex analysis) | MR | Zbl

[12] A. Porretta Existence for elliptic equations in $L^{1}$ having lower order terms with natural growth, Portugal. Math., Volume 57 (2000), pp. 179-190 | MR | Zbl

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