Capacity Solution and Numerical Approximation to a Nonlinear Coupled Elliptic System in Anisotropic Sobolev Spaces

Abstract

In this paper, we analyze the existence and the numerical simulation of a capacity solution to a coupled nonlinear elliptic system, whose unknowns are the temperature inside a semiconductor material u, and the electric potential phi. The model problem we refer to is

{-Delta((p) over right arrow)u = rho(u)vertical bar del phi vertical bar(2) in Omega

div(rho(u)del phi = 0 in Omega

phi = phi(0) on partial derivative Omega

u = 0 on partial derivative Omega

where Omega is an open bounded set of R-N, N >= 2 and Delta((p) over right arrow)u = Sigma(N)(i=1) partial derivative(i)(vertical bar partial derivative(i)u vertical bar(pi-2) partial derivative(i)u), is the (p) over right arrow -Laplacian operator. We consider the case of a nonuniformly elliptic problem.