Dirichlet problem for quasi-linear elliptic equations

Abstract

We study the Dirichlet Problem associated to the quasilinear elliptic problem $$ -sum_{i=1}^{n}frac{partial }{partial x_i}mathcal{A}_i(x,u(x), abla u(x))+mathcal{B}(x,u(x),abla u(x))=0. $$ 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.

Keywords

• Supersolution
• Dirichlet problem
• obstacle problem
• nonlinear potential theory.