Partial regularity of minimizers of p(x)-growth functionals with p(x)>1

We prove that u∈C0,α(Ω0) for some α∈(0,1) and an open set Ω0⊂Ω with Hm−γ1(Ω−Ω0)=0, where Hs denotes the s-dimensional Hausdorff measure and γ1=infΩp(x).