Electron. J. Diff. Eqns., Vol. 2002(2002), No. 82, pp. 1-18.

Dirichlet problem for quasi-linear elliptic equations

Azeddine Baalal & Nedra BelHaj Rhouma

Abstract:
We study the Dirichlet Problem associated to the quasilinear elliptic problem
$$ -\sum_{i=1}^{n}\frac{\partial }{\partial x_i}{\cal A}_i(x,u(x), \nabla u(x))+{\cal B}(x,u(x),\nabla u(x))=0. $$
Then we define a potential theory related to this problem and we show that the sheaf of continuous solutions satisfies the Bauer axiomatic theory.

Submitted April 9, 2002. Published October 2, 2002.
Math Subject Classifications: 31C15, 35B65, 35J60.
Key Words: Supersolution, Dirichlet problem, obstacle problem, nonlinear potential theory.

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  Azeddine Baalal
Departement de Mathematiques et d'Informatique,
Faculte des Sciences Ain Chock,
Km 8 Route El Jadida BP 5366 Maarif, Casablanca, Maroc.
E-mail: baalal@facsc-achok.ac.ma
Nedra BelHaj Rhouma
Institut Preparatoire aux Etudes d'Ingenieurs de Tunis,
2 Rue Jawaher Lel Nehru, 1008 Montfleury, Tunis, Tunisie.
E-mail: Nedra.BelHajRhouma@ipeit.rnu.tn

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