\(C^{1,\alpha}\) partial regularity of functions minimising quasiconvex integrals (Q1072096)

The authors prove the \(C^{1,\alpha}\) almost everywhere regularity of the minima of uniformly strictly quasi-convex functionals of the form (1) \(\int_{\Omega}F(x,u,Du)dx.\) This extends a recent result by Evans who proved the regularity for functionals with the integrand F depending only on Du. Moreover, it may be seen also as an extension of a result by \textit{M. Giaquinta} and \textit{E. Giusti} [Invent. Math. 72, 285-298 (1983; Zbl 0513.49003)] who considered functionals of type (1) by assuming on F(x,u,p) the uniformly strictly convexity in P.