JournalszaaVol. 18, No. 4pp. 1083–1100

Full C1,αC^{1, \alpha}-Regu1arity for Minimizers of Integral Functionals with LL log LL-Growth

  • Giuseppe Mingione

    Università di Parma, Italy
  • F. Siepe

    Università degli Studi di Firenze, Italy
Full $C^{1, \alpha}$-Regu1arity for Minimizers of Integral Functionals with $L$ log $L$-Growth cover
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Abstract

We consider the integral functional with nearly-linear growth ΩDulog(1+Du)dx\int_{\Omega} |Du| \mathrm {log} (1+|Du|)dx where u:ΩRnRN(n2,N1)u : \Omega \subset \mathbb R^n \to \mathbb R^N (n ≥ 2, N ≥ 1) and we prove that any local minimizer uu has locally Hölder continuous gradient in the interior of Ω\Omega thus excluding the presence of singular sets in Ω\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.

Cite this article

Giuseppe Mingione, F. Siepe, Full C1,αC^{1, \alpha}-Regu1arity for Minimizers of Integral Functionals with LL log LL-Growth. Z. Anal. Anwend. 18 (1999), no. 4, pp. 1083–1100

DOI 10.4171/ZAA/929