HOLDER CONTINUITY OF MINIMIZERS OF FUNCTIONALS WITH VARIABLE GROWTH EXPONENT

In this paper we prove the Holder continuity of local minimizers of in tegral functionals whose model is F-o(u) = integral eta\Du\(a(x))dx, w here n is an open subset of R-n, a is an element of W-1,W-s(Omega), s > n, a > 1 in Omega, and u is an element of W-loc(1,1)(Omega) is a sca lar-valued function. Following the method introduced by De Giorgi in [ 6], the proof of the main result is based on suitable Caccioppoli and Sobolev-Poincare inequalities and on a fine estimate of the supremum o f the local minimizers over small balls.