Regularity of minimizers of W1,p-quasiconvex variational integrals with (p,q)-growth

We consider autonomous integrals F[u] := integral(Omega) f (Du) dx for u : R-n superset of Omega -> R-N in themultidimensional calculus of variations, where the integrand f is a strictlyW(1,p)-quasiconvex C-2- function satisfying the (p, q)-growth conditions. gamma|A|(p) <= f(A) = Gamma(1 + |A|(q)) for every A is an element of R-nN with exponents 1 < p <= q < infinity. Under these assumptions we establish an existence result for minimizers of F in W-1,W-p(Omega; R-N) provided q < np/n-1. We prove a corresponding partial C-1,C-alpha- regularity theorem for q < p + min{2, p}/2n . This is the first regularity result for autonomous quasiconvex integrals with (p, q)-growth.