Fusco, Nicola; Hutchinson, John \(C^{1,\alpha}\) partial regularity of functions minimising quasiconvex integrals. (English) Zbl 0587.49005 Manuscr. Math. 54, 121-143 (1986). 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 M. Giaquinta and 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. Reviewer: R.Schianchi Cited in 2 ReviewsCited in 40 Documents MSC: 49J10 Existence theories for free problems in two or more independent variables 26B25 Convexity of real functions of several variables, generalizations 49J45 Methods involving semicontinuity and convergence; relaxation 35D10 Regularity of generalized solutions of PDE (MSC2000) Keywords:regularity; minima; quasi-convex functionals Citations:Zbl 0513.49003 PDFBibTeX XMLCite \textit{N. Fusco} and \textit{J. Hutchinson}, Manuscr. Math. 54, 121--143 (1986; Zbl 0587.49005) Full Text: DOI EuDML References: [1] L.C. Evans, Quasiconvexity and Partial Regularity in the Calculus of Variations, University of Maryland, Department of Mathematics, preprint MD84-45Le, (1984) [2] I. Ekeland, Nonconvex Minimization Problems,Bull. Amer. Math. Soc. 1 (1979), 443-474 · Zbl 0441.49011 [3] M. Giaquinta,Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Mathematics Studies 105, Princeton Univ. Press, Princeton, New Jersey, (1983) · Zbl 0516.49003 [4] M. Giaquinta and E. Giusti, Differentiability of Minima of Nondifferentiable Functionals,Inventiones Math. 72 (1983), 285-298 · Zbl 0513.49003 [5] C.B. Morrey Jr.,Multiple Integrals in the Calculus of Variations, Springer-Verlag, Heidelberg, New York, (1966) · Zbl 0142.38701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.