Partial regularity of minimizers of asymptotically convex functionals with p(x)-growth

We consider vectorial minimizers of the integral functional integral(Omega) f(x, u, Du) dx, where the function (x, u, xi) bar right arrow f (x, u, xi) is asymptotically related to a simpler function (x, u, xi) bar right arrow a(x, u)vertical bar xi vertical bar(p(x)). Thus, we consider asymptotically convex integral functionals in the p(x)-growth setting. We demonstrate that minimizers are almost everywhere Holder continuous, in a manner that mimics that simpler p-growth setting.