Boundary regularity for elliptic systems with p,q-growth

Abstract

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 Ω and homogeneous Dirichlet data on some part Γ⊂∂Ω of the boundary. For the integrand we assume only a non-standard p,q-growth condition. We establish Lipschitz regularity of minimizers up to Γ, provided the gap between the growth exponents p and q is not too large, more precisely if 1<p≤q<p(1+2n). To our knowledge, this is the first boundary regularity result under a non-standard p,q-growth condition.