Partial regularity of minimizers of quasiconvex integrals (Q1076954)

The authors consider variational integrals \(\int_{\Omega}f(x,u,Du)dx\) with f(x,u,p) growing polynomially, of class \(C^ 2\) in p and Hölder continuous in (x,u). Under the main assumption that f(x,u,p) is uniformly strictly quasiconvex they prove that each minimizer is of class \(C^{1,\mu}\) in an open set \(\Omega_ 0\subset \Omega\) such that \(meas(\Omega -\Omega_ 0)=0\).