EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 4, pp. 1083-1100 (1999)

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Full $C^{1,\alpha}$-Regularity for Minimizers of Integral Functionals with $L\log L$-Growth

G. Mingione and F. Siepe

G. 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.it

Abstract: We consider the integral functional with nearly-linear 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

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Electronic fulltext finalized on: 7 Aug 2001. This page was last modified: 9 Nov 2001.

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