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

We prove partial regularity of minimizers u for functionals of the following type A(u) = integral(ohm)[(Alpha(alpha beta)(ij)(x,u,)D(alpha)u(i) D(beta)u(j))(p(x)/2) + g(x,u,Du)] dx, assuming that Alpha(alpha beta)(ij)(x, u) and p(x) are sufficiently smooth and that p(x) > 1. We prove that u is an element of C-0,C-alpha(ohm(0)) for some alpha is an element of (0,1) and an open set ohm(0) C ohm with Eta(m-n)(ohm - ohm(0)) = 0, where Eta(s) denotes the s -dimensional Hausdorff measure and gamma(1) = inf ohm p(x). (C) 2017 Elsevier Ltd. All rights reserved.