An existence theorem for weak solutions for a class of elliptic partial differential systems in general Orlicz-Sobolev spaces

I prove the existence of a weak solution for the Dirichlet problem of a class of elliptic partial differential systems - partial derivative A(alpha)(i)/partial derivative x(alpha) (x, u(x), Du(x)) + B-i (x, u(x), Du(x)) = 0 in general Orlicz-Sobolev spaces (W0LM)-L-1 (Omega, R-N) where i = 1, N, alpha 1,..., n, u : Omega -> R-N is a vector-valued function, and the summation convention is used throughout with i, j running from 1 to N and alpha, beta running from 1 to n. (C) 2007 Elsevier Ltd. All rights reserved.