Variational Integrals on Orlicz–Sobolev Spaces

We consider vector functions u : R^n ⊃ Ω → R^N minimizing variational integrals of the form ∫Ω G( u)dx with convex density G whose growth properties are described in terms of an N -function A : (0, ∞) → (0, ∞) with limsup t → ∞ A(t)t–2 < ∞ . We then prove - under certain technical assumptions on G - full regularity of u provided that n = 2 , and partial C^1 -regularity in the case n ≥ 3 . The main feature of the paper is that we do not require any power growth of G .