Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 82, pp. 1-18.
Title: Dirichlet problem for quasi-linear elliptic equations
Authors: Azeddine Baalal (Faculte des Sciences Ain Chock, Maroc)
Nedra BelHaj Rhouma (Inst. Prep. aux Etudes d'Ing. de Tunis, Tunisie)
Abstract:
We study the Dirichlet Problem associated to the quasilinear
elliptic problem
$$
-\sum_{i=1}^{n}\frac{\partial }{\partial x_i}\mathcal{A}_i(x,u(x),
\nabla u(x))+\mathcal{B}(x,u(x),\nabla u(x))=0.
$$
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.