Acta Mathematica

On the regularity of the minima of variational integrals

Mariano Giaquinta and Enrico Giusti

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Article information

Source
Acta Math. Volume 148 (1982), 31-46.

Dates
Received: 6 June 1981
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890156

Digital Object Identifier
doi:10.1007/BF02392725

Zentralblatt MATH identifier
0494.49031

Rights
1982 © Almqvist & Wiksell

Citation

Giaquinta, Mariano; Giusti, Enrico. On the regularity of the minima of variational integrals. Acta Math. 148 (1982), 31--46. doi:10.1007/BF02392725. https://projecteuclid.org/euclid.acta/1485890156


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References

  • Attouch, H. & Sbordone, C. Asymptotic limits for perturbed functionals of calculus of variations: Ricerche Mat., 29 (1981), 85–124.
  • Boyarskii, B. V., Generalized solutions of a system of differential equations of the first order of elliptic type with discontinuous coefficients. Mat. Sb., 43, (1957), 451–503.
  • Campanato, S., Equazioni ellittiche del secondo ordine e spazi 45-1. Ann. Mat. Pura Appl., 69 (1965), 321–382.
  • De Giorgi, E., Sulla differenziabilità e l'analiticità degli integrali multipli regolari. Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (3), 3 (1957), 25–43.
  • —, Un esempio di estremali discontinue per un problema variazionale di tipo ellittico Boll. Un. Mat. Ital. Ser. IV, 1 (1968), 135–138.
  • Frehse, J., A discontinuous solution of a midly nonlinear elliptic system. Math. Z., 134 (1973), 229–230.
  • —, A note on the Hölder continuity of solutions of variational problems. Abh. Math. Sem. Univ. Hamburg, 43 (1975), 59–63.
  • Gehring, F. W., The Lp-integrability of the partial derivatives of a quasi conformal mapping. Acta Math., 130 (1973), 265–277.
  • Giaquinta, M. & Giusti, E., Nonlinear elliptic systems with quadratic growth. Manuscripta Math., 24 (1978), 323–349.
  • Giaquinta, M. & Modica, G., Regularity results for some classes of higher order non linear elliptic systems. J. Reine Angew. Math., 311/312 (1979), 145–169.
  • —, Almost-everywhere regularity results for solutions of non linear elliptic systems. Manuscripta Math., 28 (1979), 109–158.
  • Gilbarg, D. & Trudinger, N. S., Elliptic partial differential equations of second order. Springer-Verlag, Berlin (1977).
  • Hildebrandt, S. & Widman, K.-O., Some regularity results for quasilinear elliptic systems of second order. Math. Z., 142 (1975), 67–86.
  • Hildebrandt, S., Kaul, H. & Widman, K.-O., An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math., 138 (1977), 1–16.
  • Ivert, P. A., Regularitätsuntersuchungen von Lösungen elliptischer Systeme von quasilinearen Differentialgleichungen zweiter Ordnung. Manuscripta Math., 30 (1979), 53–88.
  • —, On quasilinear elliptic systems in diagonal form. Math. Z., 170 (1980), 283–286.
  • Ladyženskaya, O. A. & Ural'ceva, N. N., Linear and quasilinear elliptic equations. New York and London, Academic Press (1968).
  • Meier, M., Liouville theorems for nonlinear elliptic equations and systems. Manuscripta Math. 29 (1979), 207–228.
  • Meyers, N. G., An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa, (3) 17 (1963), 189–206.
  • Morrey, C. B., Multiple integrals in the calculus of variations. Springer, Berlin (1968).
  • Skrypnik, I. V., Nonlinear elliptic equations of higher order (in Russian). Kiev (1973).
  • Struwe, M., A counterexample in elliptic regularity theory., Manuscripta Math., 34 (1981), 85–92.
  • Todorov, T. G., Smoothness of generalized solutions of quasilinear elliptic systems of higher order. Problemy Mathematičeskogo Analiza, 5 (1975), 180–191.
  • Widman, K.-O., Hölder continuity of solutions of elliptic systems, Manuscripta Math. 5 (1971), 299–308.
  • Wiegner, M.Das Existenz- und Regularitätsproblem bei Systemen nichtlinearer elliptischer Differentialgleichungen Habilitationsschrift, Bochum 1977.
  • Wiegner, M. On two-dimensional elliptic systems with a one-sided condition. Preprint.