Variational inequalities for energy functionals with nonstandard growth conditions

We consider the obstacle problem{minimize????????I(u)=?OG(?u)dx??among functions??u:O?Rsuch?that???????u|?O=0??and??u=F??a.e.for a given functionF?C2(O¯),F|?O<0and a bounded Lipschitz domainOinRn. The growth properties of the convex integrandGare described in terms of aN-functionA:[0,8)?[0,8)withlimt?8¯A(t)t-2<8. Ifn=3, we prove, under certain assumptions onG,C1,8-partial regularity for the solution to the above obstacle problem. For the special case whereA(t)=tln(1+t)we obtainC1,a-partial regularity whenn=4. One of the main features of the paper is that we do not require any power growth ofG.