We study autonomous integrals
F[u] := ∫Ω ƒ(Du) dx for u : ℝn ⊃ Ω → ℝN
in the multidimensional calculus of variations, where the integrand ƒ is a strictly quasiconvex function satisfying the (p, q)-growth conditions
γ|ξ|p ≤ ƒ(ξ) ≤ Γ(1 + |ξ|q)
with exponents . Imposing the additional assumption that ƒ resembles the degenerate behavior of the p-energy density, we establish a partial C
1,α-regularity theorem for F-minimizers and a similar theorem for minimizers of a relaxed functional.
Our results cover the model case of polyconvex integrands
where h is a smooth convex function with -growth