Lipschitz continuity for energy integrals with variable exponents

A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set Ω ⊂ R^n , with variable exponent p(x) in the Sobolev class W1,r_loc (Ω) for some r > n , is locally Lipschitz continuous in Ω and an a priori estimate holds.