Partial and Full Boundary Regularity for Minimizers of Functionals with Nonquadratic Growth

We consider regularity at the boundary for minimizers of variational integrals whose integrands have nonquadratic growth in the gradient. Under relatively mild assumptions on the coefficients we obtain a partial regularity result. For coefficients of a more particular type, namely those satifying a particular splitting condition, we obtain full boundary regularity. The results are new for the situation under consideration. The key ingredients are a new version of the usual Gehring-type lemma, and a careful adaptation of the technique of dimension-reduction to the current setting