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$.
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Received December 1998
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Esposito, L., Mingione, G. Partial regularity for minimizers of convex integrals with L log L-growth. NoDEA, Nonlinear differ. equ. appl. 7, 107–125 (2000). https://doi.org/10.1007/PL00001420
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DOI: https://doi.org/10.1007/PL00001420