Boundary regularity for elliptic systems with p, q-growth

We investigate the boundary regularity of minimizers of convex integral functionals with nonstandard p, q-growth and with Uhlenbeck structure. We consider arbitrary convex domains omega and homogeneous Dirichlet data on some part Gamma subset of partial differential omega of the boundary. For the integrand we assume only a non-standard p, q-growth condition. We establish Lipschitz regularity of minimizers up to Gamma, provided the gap between the growth exponents p and q is not too large, more precisely if 1 < p < q < p(1 + n2 ). To our knowledge, this is the first boundary regularity result under a non-standard p, q-growth condition.