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manuscripta mathematica

, Volume 28, Issue 1–3, pp 109–158 | Cite as

Almost-everywhere regularity results for solutions of non linear elliptic systems

  • Mariano Giaquinta
  • Giuseppe Modica
Article

Abstract

We prove almost-everywhere regularity of weak solutions of non linear elliptic systems of arbitrary order.

Keywords

Weak Solution Number Theory Algebraic Geometry Topological Group Elliptic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    CAMPANATO S.: Proprietà di hölderianità di alcune classi di funzioni. Ann. S.N.S. Pisa, 17, 175–188 (1963)Google Scholar
  2. [2]
    CAMPANATO S.: Equazioni ellittiche del II ordine e spazi ℒ2, λ. Ann. Mat. Pura e Appl., 69, 321–382 (1965).Google Scholar
  3. [3]
    CAMPANATO S.: Alcune osservazioni relative alle soluzioni di equazioni ellittiche di ordine 2m. Atti Convegno Equaz. Der. Parz., Bologna (1967)Google Scholar
  4. [4]
    CAMPANATO S.: Partial Hölder continuity of the gradient of solutions of some nonlinear elliptic systems. To appear in Rend. Sem. Mat. Padova.Google Scholar
  5. [5]
    CANFORA A.: Teorema del massimo modulo e teorema di esistenza per il problema di Dirichlet relativo ai sistemi fortemente ellittici. Ricerche di Mat., 15, 249–294 (1966)Google Scholar
  6. [6]
    DE GIORGI E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico. Boll. UMI, 4, 135–137 (1968)Google Scholar
  7. [7]
    GIAQUINTA M.: A counter-example to the boundary regularity of solutions to elliptic quasilinear systems. Manuscripta math. 24, 217–220 (1978)Google Scholar
  8. [8]
    GIAQUINTA M., GIUSTI E.: Nonlinear elliptic systems with quadratic growth. Manuscripta math. 24, 323–349 (1978)Google Scholar
  9. [9]
    GIAQUINTA M., MODICA G.: Regularity results for some classes of higher order non linear elliptic systems. To appearGoogle Scholar
  10. [10]
    GIUSTI E.: Precisazione delle funzioni di H e singolarità delle soluzioni deboli di sistemi ellittici non lineari. Boll. UMI 2, 71–76 (1969)Google Scholar
  11. [11]
    GIUSTI E.: Regolarità parziale, delle soluzioni di sistemi ellittici quasi lineari di ordine arbitrario. Ann. S.N.S. Pisa 23, 115–141 (1969)Google Scholar
  12. [12]
    GIUSTI E.: Un'aggiunta alla mia nota: Regolarità parziale delle soluzioni di sistemi ellittici quasilineari di ordine arbitrario. Ann. S.N.S. Pisa 27 161–166 (1973)Google Scholar
  13. [13]
    GIUSTI E., MIRANDA M.: Un esempio di soluzioni discontinue per un problema di minimo relativo ad un integrale regolare del calcolo delle variazioni. Boll. UMI 2, 1–8 (1968)Google Scholar
  14. [14]
    GIUSTI E., MIRANDA M.: Sulla regolarità delle soluzioni deboli di sistemi ellittici quasilineari. Arch. Rat. Mech. and Anal. 31, 173–184 (1968)Google Scholar
  15. [15]
    HEINZ E.: Ein Regularitätssatz für schwache Lösungen nicht-linearer elliptischer Systeme. Göttinger Nachrichten, Nr. 1 (1975)Google Scholar
  16. [16]
    HILDEBRANDT S., WIDMAN K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z. 142, 67–86 (1975)Google Scholar
  17. [17]
    HILDEBRANDT S., WIDMAN K.-O.: On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. S.N.S. Pisa 1, 145–178 (1977)Google Scholar
  18. [18]
    IVERT P.-A.: Regularitätsuntersuchungen von Lösungen elliptischer Systeme von quasilinearen Differentialgleichungen zweiter Ordnung. Linköping Studies in Science and Technology Dissertations No. 31 (1978)Google Scholar
  19. [19]
    LADYZENSKAYA O. A., URAL'TSEVA N. N.: Linear and quasilinear elliptic equations. New-York Academic Press (1968)Google Scholar
  20. [20]
    MORREY C. B. Jr.: Exixtence and differentiability theorems for the solutions of variational problems for multiple integrals. Bull. A.M.S. 46, 439–458 (1940) 46, 439–458 (1940)Google Scholar
  21. [21]
    MORREY C. B. Jr.: Multiple integral problems in the calculus of variations and related topics. Univ. of California Publ. in Math., new ser. 1, 1–130 (1943)Google Scholar
  22. [22]
    MORREY, C. B. Jr.: Multiple integrals in the calculus of variations. Berlin Springer-Verlag (1966)Google Scholar
  23. [23]
    MORREY C. B. Jr.: Partial regularity results for non linear elliptic systems. Journ. Math. and Mech. 17, 649–670 (1968)Google Scholar
  24. [24]
    MORREY C. B. Jr.: Differentiability theorems for non linear elliptic equations. Actes Congrès intern. Math. (1970).Google Scholar
  25. [25]
    NEČAS J.: Example of an irregular solution to a non linear elliptic system with analitic coefficients and conditions for regularity. Beiträge zur Analysis (1977)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Mariano Giaquinta
    • 1
  • Giuseppe Modica
    • 2
  1. 1.Istituto di Matematica Applicata, Facoltà di IngegneriaUniversità di FirenzeFirenze(Italia)
  2. 2.Istituto Matematico dell'UniversitàPisa(Italia)

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