Partial regularity for minimizers of convex integrals with L log L-growth

Abstract.

We prove $C^{1, \alpha}$-partial regularity of minimizers \(u\in W^{1, 1}_{loc} (\Omega; {\Bbb R}^N)$, with \(\Omega\subset {\Bbb R}^n$, for a class of convex integral functionals with nearly linear growth whose model is $\int_\Omega\log(1+|Du|)|Du|dx$ In this way we extend to any dimension n a previous, analogous, result in [FS] valid only in the case \(n\leq 4$.