Local boundedness for minimizers of some polyconvex integrals (Q522188)

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.