Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions

E. Acerbi & N. Fusco, A regularity theorem for minimizers of quasiconvex integrals, Arch. Rational Mech. Analysis 99 (1987), 261–281.

H. Brezis, Analyse fonctionnelle, Théorie et applications, Masson, 1983.

E. de Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat. 3 (1957), 25–43.

M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Math. Studies 105, Princeton Univ. Press, 1983.

M. Giaquinta, Growth conditions and regularity, a counterexample, Preprint Univ. Bonn, July 1987, to appear in Manuscripta Math.

M. Giaquinta & E. Giusti, On the regularity of minima of variational integrals, Acta Math. 148 (1982), 31–46.

D. Gilbarg, & N. S. Trudinger, Elliptic partial differential equations of second order, Grundl. Math. Wiss. 224, Springer-Verlag, 1977.

E. Giusti, Equazioni ellittiche del secondo ordine, Quaderni UMI n. 6, Pitagora Ed., 1978.

O. Ladyzhenskaya & N. Ural'tseva, Linear and quasilinear elliptic equations, Math, in Science and Engineering 46, Academic Press, 1968.

P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math. 51 (1985), 1–28.

P. Marcellini, On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. Henri Poincaré, Analyse non linéaire 3 (1986), 391–409.

P. Marcellini, Un exemple de solution discontinue d'un problème variationnel dans le cas scalaire, Manuscript, September 1987.

C. B. Morrey, Multiple integrals in the calculus of variations, Grundl. Math. Wiss. 130, Springer-Verlag, 1966.

J. Moser, A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Communications Pure Appl. Math. 13 (1960), 457–468.