Holder continuity of local minimizers of vectorial integral functionals

study the regularity of vector-valued local minimizers in W-1,W-p, p > 1, of the integral functional mu --> integral(Omega) [(mu(2) + \Dmu\(2))(p/2) + f (x, mu, \Dmu\)] dx, where Omega is an open set in R-N and f is a continuous function, convex with respect to the last variable, such that 0 less than or equal to f(x, mu, t) less than or equal to C(1 + t(P)). We prove that if f = f (x, t), or f = f (x, mu, t) and p greater than or equal to N, then local minimizers are locally Holder continuous for any exponent less' than 1. If f = f (x, mu, t) and p < N then local minimizers are Holder continuous for every exponent less than 1 in an open set Omega(0) such that the Hausdorff dimension of Omega \ Omega(0) is less than N - p.