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Partial regularity of minimizers of quasiconvex integrals. (English) Zbl 0594.49004
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 \(meas(\Omega -\Omega_ 0)=0\).
Reviewer: R.Schianchi

MSC:
49J45 Methods involving semicontinuity and convergence; relaxation
26B25 Convexity of real functions of several variables, generalizations
35B65 Smoothness and regularity of solutions to PDEs
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