On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order

Stefan Hildebrandt; Kjell-Ove Widman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1977)

  • Volume: 4, Issue: 1, page 145-178
  • ISSN: 0391-173X

How to cite

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Hildebrandt, Stefan, and Widman, Kjell-Ove. "On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.1 (1977): 145-178. <http://eudml.org/doc/83742>.

@article{Hildebrandt1977,
author = {Hildebrandt, Stefan, Widman, Kjell-Ove},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {145-178},
publisher = {Scuola normale superiore},
title = {On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order},
url = {http://eudml.org/doc/83742},
volume = {4},
year = {1977},
}

TY - JOUR
AU - Hildebrandt, Stefan
AU - Widman, Kjell-Ove
TI - On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1977
PB - Scuola normale superiore
VL - 4
IS - 1
SP - 145
EP - 178
LA - eng
UR - http://eudml.org/doc/83742
ER -

References

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  1. [1] R. Baire, Sur la représentation des fonctions discontinues, Acta Math., 30 (1906), pp. 1-48 and 32 (1909), pp. 97-176. Zbl36.0453.01JFM40.0443.03
  2. [2] C. Carathéodory, Vorlesungen über reelle Funktionen, Leipzig und Berlin, Teubner, 1927. JFM53.0225.16
  3. [3] S. Hildebrandt - K.-O. Widman, Some regularity results for quasilinear elliptic systems of second order, Math. Z., 142 (1975), pp. 67-86. Zbl0317.35040MR377273
  4. [4] S. Hildebrandt - K.-O. Widman, On a theorem of Ladyženskaya and Ural'ceva, Dept. Mathematics Linköping Report, March 1975. 
  5. [5] S. Hildebrandt - H. Kaul - K.-O. Widman, An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math. (to appear). Zbl0356.53015MR433502
  6. [6] O.A. Lady - N.N. Ural'ceva, Linear and quasilinear elliptic equations, New York and London, Academic Press, 1968 (English translation of the first Russian edition 1964). Zbl0164.13002MR244627
  7. [7] W. Littman - G. Stampacchia - H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa, Sci. fis. mat., III ser., 17 (1963), pp. 43-77. Zbl0116.30302MR161019
  8. [8] C.B. Morrey, Multiple integrals in the calculus of variations, Berlin - Heidelberg - New York, Springer, 1966. Zbl0142.38701MR202511
  9. [9] J. Moser, A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math., 13 (1960), pp. 457-468. Zbl0111.09301MR170091
  10. [10] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math., 14 (1961), pp. 577-591. Zbl0111.09302MR159138
  11. [11] E. Sperner, Ein neuer Regularitätssatz für gewisse Systeme nichtlinearer elliptischer Differentialgleichungen, Math. Z. (to appear). Zbl0319.35037MR415050
  12. [12] K.-O. Widman, The singularity of the Green function for non-uniformly elliptic partial differential equations with discontinuous coefficients, Uppsala University, Dec. 1970. 
  13. [13] K.-O. Widman, Hölder continuity of solutions of elliptic systems, Manuscripta Math., 5 (1971), pp. 299-308. Zbl0223.35044MR296484
  14. [14] M. Wiegner, Über die Regularität schwacher Lösungen gewisser elliptischer Systeme, Manuseripta Math., 15 (1975), pp. 365-384. Zbl0312.35035MR509086
  15. [15] M. Wiegner, Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme, Math. Z., 147 (1976), pp. 21-28. Zbl0316.35039MR407430
  16. [16] M. Wiegner, A-priori Schranken für Lösungen gewisser elliptischer Systeme, Manuscripta Math., 18 (1976), pp. 279-297. Zbl0323.35032MR402272

Citations in EuDML Documents

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  1. Jérôme Busca, Boyan Sirakov, Harnack type estimates for nonlinear elliptic systems and applications
  2. Sergio Campanato, Partial Hölder continuity of the gradient of solutions of some nonlinear elliptic systems
  3. M. Giaquinta, S. Hildebrandt, Estimation à priori des solutions faibles de certains systèmes non linéaires elliptiques
  4. Michael Pingen, Regularity results for degenerate elliptic systems
  5. Peter Tolksdorf, On some parabolic variational problems with quadratic growth
  6. Jens Frehse, Umberto Mosco, Irregular obstacles and quasi-variational inequalities of stochastic impulse control
  7. Michael Struwe, Some regularity results for quasi-linear parabolic systems
  8. Bernhard Kawohl, On Liouville theorems, continuity and Hölder continuity of weak solutions to some quasilinear elliptic systems

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