Existence of solutions for a quasilinear elliptic system with variable exponent

Abstract

We consider the following quasilinear elliptic system in a Sobolev space with variable exponent: [-text{div}(a(|Du|)Du)=f,] where $a$ is a $C^1$-function and $fin W^{-1,p'(x)}(Omega;R^m)$. We use the theory of Young measures and weak monotonicity conditions to obtain the existence of solutions.