Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 10831100 (1999) 

Full $C^{1,\alpha}$Regularity for Minimizers of Integral Functionals with $L\log L$GrowthG. Mingione and F. SiepeG. Mingione: Dept. Math. Univ., Via D'Azeglio 85/A, 43100 Parma, Italy, mingione@prmat.math.unipr.it ; / F. Siepe: Dept. Math. Univ., Viale Morgagni 67/A, 50134 Firenze, Italy, siepe@alibaba.math.unifi.itAbstract: We consider the integral functional with nearlylinear growth $\int_\Omega Du\log(1 + Du)dx$ where $u: \, \Omega \subset \R^n \to \R^N \ (n \ge 2,\, N \ge 1)$ and we prove that any local minimizer $u$ has locally Hölder continuous gradient in the interior of $\Omega$ thus excluding the presence of singular sets in $\Omega$. This functional has recently been considered by several authors in connection with variational models for problems from the theory of plasticity with logarithmic hardening. We also give extensions of this result to more general cases. Keywords: integral functionals, minimizers, $L\log L$growth, Hölder continuity Classification (MSC2000): 49N60, 35J50 Full text of the article:
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