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

Aharouch, Lahsen; Akdim, Youssef

doi:10.5802/ambp.185

Existence of solutions of degenerated unilateral problems with

L^{1}

data

Aharouch, Lahsen ¹ ; Akdim, Youssef ¹

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

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

Résumé
Abstract

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 Zbl

DOI : 10.5802/ambp.185

Affiliations des auteurs :

Aharouch, Lahsen ¹ ; Akdim, Youssef ¹

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

@article{AMBP_2004__11_1_47_0,
     author = {Aharouch, Lahsen and Akdim, Youssef},
     title = {Existence of solutions of degenerated unilateral problems with $L^1$ data},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {47--66},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {11},
     number = {1},
     year = {2004},
     doi = {10.5802/ambp.185},
     zbl = {02207858},
     mrnumber = {2077238},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/ambp.185/}
}

TY  - JOUR
AU  - Aharouch, Lahsen
AU  - Akdim, Youssef
TI  - Existence of solutions of degenerated unilateral problems with $L^1$ data
JO  - Annales mathématiques Blaise Pascal
PY  - 2004
SP  - 47
EP  - 66
VL  - 11
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - http://archive.numdam.org/articles/10.5802/ambp.185/
DO  - 10.5802/ambp.185
LA  - en
ID  - AMBP_2004__11_1_47_0
ER  -

%0 Journal Article
%A Aharouch, Lahsen
%A Akdim, Youssef
%T Existence of solutions of degenerated unilateral problems with $L^1$ data
%J Annales mathématiques Blaise Pascal
%D 2004
%P 47-66
%V 11
%N 1
%I Annales mathématiques Blaise Pascal
%U http://archive.numdam.org/articles/10.5802/ambp.185/
%R 10.5802/ambp.185
%G en
%F AMBP_2004__11_1_47_0

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

Bibliographie
Cité par

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

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

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

[4] Bénilan, P.; Boccardo, L.; Gallouët, T.; Gariepy, R.; Pierre, M.; Vazquez, J. L. 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] Boccardo, L.; Gallouët, T. Non-linear Elliptic Equations with right hand side Measures, commun. In partial Differential Equations, Volume 17 (1992), pp. 641-655 | MR | Zbl

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

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

[9] Dalmaso, G.; Murat, F.; Orsina, L.; Prignet, A. 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] Drabek, P.; Kufner, A.; Nicolosi, F. Nonlinear elliptic equations, singular and degenerate cases, University of West Bohemia, 1996

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

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

Cité par Sources :