A general regularity theorem for functionals with φ-growth

We prove C1,αC1,α-regularity for local minimizers of functionals∫Ωφ(|∇u|)dx, where φ is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function φ   only the (Δ2)(Δ2)-condition and φ″(t)⩾ϵˆφ′(t)t for a positive constant ϵˆ (and of course a Hölder-condition for the second derivatives).