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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
##### Keywords:
quasiconvexity; variational integrals; minimizer
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##### References:
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