Dirichlet Problem for Quasi-Linear Elliptic Equations
Rhouma, Nedra BelHaj
Southwest Texas State University, Department of Mathematics
We study the Dirichlet Problem associated to the quasilinear elliptic problem -Σni=1 ∂/ ∂xi Ai(x, u(x), ∇u(x)) + B(x, u(x), ∇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.
Supersolution, Dirichlet problem, Obstacle problem, Nonlinear potential theory
Baalal, A., Rhouma, N. B. (2002). Dirichlet problem for quasi-linear elliptic equations. <i>Electronic Journal of Differential Equations, 2002</i>(82), pp. 1-18.