Higher integrability of very weak solutions of systems of 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)-Laplacean system div |Du|p(x)−2Du = div |F|p(x)−2F , i.e. we show that, for small enough, a function which solves the system and has bounded p(x)(1 − )- energy satisfies |Du|p(x) ∈ L1 loc. © 2007 Elsevier Inc. All rights reserved.