Advertisement

Arkiv för Matematik

, Volume 19, Issue 1–2, pp 117–122 | Cite as

On the Hölder continuity of monotone extremals in the “borderline case”

  • Peter Lindqvist
Article
  • 36 Downloads

Keywords

Quasiconformal Mapping Borderline Case Quasiregular Mapping Concentric Ball H61der Continuity 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Finn, R., &Serrin, J., On the Hölder continuity of quasiconformal and elliptic mappings,Trans. Amer. Math. Soc. 89 (1958), pp. 1–15.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Gehring, F., Rings and quasiconformal mappings in space,Trans. Amer. Math. Soc. 103 (1962), pp. 353–393.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Granlund, S.,On regular solutions for a variational problem defined in Sobolev spaces, Report-HTKK-Mat-A 114 (1977), pp. 1–18.Google Scholar
  4. 4.
    Granlund, S., Harnack's inequality in the borderline case,Ann. Acad. Sci. Fenn. Ser. AI (to appear).Google Scholar
  5. 5.
    Ladyzhenskaya, O., &Ural'tseva, N.,Linear and quasi-linear elliptic equations, Academic Press, New York-London, 1968.Google Scholar
  6. 6.
    Lindqvist, P.,On Liouville's theorem for locally quasiregular mappings in R n, Report-HTKK-Mat-A151 (1979), pp. 1–11.Google Scholar
  7. 7.
    Martio, O., Equicontinuity theorem with an application to variational integrals,Duke Math. J. 42 (1975), pp. 569–581.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Martio, O., Rickman, S., &Väisälä, J., Definitions for quasiregular mappings,Ann. Acad. Sci. Fenn. Ser. AI 448 (1969), pp. 1–40.Google Scholar
  9. 9.
    Martio, O., Rickman, S., &Väisälä, J., Distortion and singularities of quasiregular mappings,Ann. Acad. Sci. Fenn. Ser. AI 465 (1970), pp. 1–13.Google Scholar
  10. 10.
    Morrey, Ch.,Multiple integrals in the calculus of variations. Springer-Verlag, Berlin-Heidelberg-New York, 1966.MATHGoogle Scholar
  11. 11.
    Mostow, G., Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms,Inst. Hautes Etudes Sci. Publ. Math. 34 (1968), pp. 53–104.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Reshetnyak, Yu., General theorems on semicontinuity and on convergence with a functional,Siberian Math. J. 8.5 (1967), pp. 801–807 (English translation).CrossRefGoogle Scholar
  13. 13.
    Reshetnyak, Yu., Mappings with bounded deformation as extremals of Dirichlet type integrals,Siberian Math. J. 9 (1968), pp. 487–498 (English translation).MATHCrossRefGoogle Scholar
  14. 14.
    Serrin, J., Local behaviour of solutions of quasi-linear equations,Acta Math. 111 (1964), pp. 247–302.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Widman, K.-O., Hölder continuity of solutions of elliptic systems,Manuscripta Math. 5 (1971), pp. 299–308.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1981

Authors and Affiliations

  • Peter Lindqvist
    • 1
  1. 1.Matematiska InstitutionenTekniska Högskolan i HelsingforsESBO 15Finland

Personalised recommendations