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

We consider vectorial minimizers of the integral functionalintegral(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 alpha(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.