Local boundedness for minimizers of some polyconvex integrals. (English) Zbl 1365.49035
The authors are concerned with the study of local regularity of minimisers for variational integrals
\[
I(u,\Omega)=\int_\Omega f(Du)dx,
\]
where \(u:\Omega\subset {\mathbb R}^3\to {\mathbb R}^3\) and \(f\) is polyconvex. Under some structure assumptions on the energy density, the main results of the papers establish that local minimizers \(u\) satisfy \(u\in L^\infty_{\mathrm{loc}}(\Omega,{\mathbb R}^3)\). The approach relies on Caccioppoli type estimates combined with De Giorgi iteration techniques.
Reviewer: Marius Ghergu (Dublin)
MSC:
| 49N60 | Regularity of solutions in optimal control |
| 35J50 | Variational methods for elliptic systems |
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