Calculus of Variations and Geometric Measure Theory
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L. Esposito - G. Mingione

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

created by mingione on 30 Sep 2012


Published Paper

Inserted: 30 sep 2012
Last Updated: 30 sep 2012

Journal: Non. Diff. Equ. Appl.
Volume: 7
Pages: 107-125
Year: 2000


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

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