Calculus of Variations and Geometric Measure Theory
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G. Mingione - F. Siepe

Full $C^{1,α}$-regularity for minimizers of integral functionals with Llog L-growth

created by mingione on 05 Oct 2012
modified on 15 Oct 2012


Published Paper

Inserted: 5 oct 2012
Last Updated: 15 oct 2012

Journal: ZAA
Volume: 18
Pages: 1083-1100
Year: 1999


We consider the following integral functional with nearly-linear growth \[ \int_{\Omega}
) \ dx \] where $u:\ \Omega \subset \Bbb R^{n} \rightarrow \Bbb R^{N}, n\ge 2, \ N\geq 1$ and we prove that any local minimizer $u$ has locally H\"older 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.


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