Higher integrability of very weak solutions of systems of p(x)p(x)-Laplacean type

We prove higher integrability of very weak solutions of a class of nonlinear elliptic systems whose model is the p(x)p(x)-Laplacean systemdiv(|Du|p(x)−2Du)=div(|F|p(x)−2F),div(|Du|p(x)−2Du)=div(|F|p(x)−2F), i.e. we show that, for ϵ small enough, a function which solves the system and has bounded p(x)(1−ϵ)p(x)(1−ϵ)-energy satisfies |Du|p(x)∈Lloc1.