Skip to main content
SpringerLink
Log in

On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Summary

The Hölder continuity of bounded weak solutions of quasilinear parabolic systems with main part in diagonal form is proved via a “parabolic hole-filling technique”.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ARONSON, D.G.: Non-negative solutions of linear parabolic equations. Ann. Sc. Norm. Sup. Pisa22, 607–694 (1968)

    Google Scholar 

  2. CAMPANATO, S.: Proprietá die hölderianitá di alcune classi di funzioni, Ann. Sc. Norm. Sup. Pisa17, 175–188 (1963)

    Google Scholar 

  3. DA PRATO, G.: Spazi(p, θ)(Ω, δ) e loro proprietá. Ann. Mat. Pura Appl.69, 383–392 (1965)

    Google Scholar 

  4. FREHSE, J. - MOSCO, U.: Variational inequalities with one-sided irregular obstacles, manusc. math.28, 219–233 (1979)

    Google Scholar 

  5. FREHSE, J.: On two-dimensional quasilinear elliptic systems, manusc. math.28, 21–49 (1979)

    Google Scholar 

  6. FREHSE, J.: Capacity methods in the theory of partial differential equations, to appear

  7. HILDEBRANDT, S. - WIDMAN, K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z.142, 67–86 (1975)

    Google Scholar 

  8. HILDEBRANDT, S. - WIDMAN, K.-O.: On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Sc. Norm. Sup. Pisa Ser. 4,4, 145–178 (1977)

    Google Scholar 

  9. KUFNER, A. - JOHN, O. - FUCIK, A.: Function spaces. Academia, Prague (1977)

    Google Scholar 

  10. LADYSHENSKAYA, O.A. - SOLONNIKOV, V.A. - URAL'CEVA, N.N.: Linear and quasilinear equations of parabolic type. Translations Math. Monogr.23, AMS, Providence, R.I. (1968)

    Google Scholar 

  11. LADYSHENSKAYA, O.A. - URAL'CEVA, N.N.: Linear and quasilinear elliptic equations. Academic Press, New York (1968)

    Google Scholar 

  12. MOSER, J.: A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math.17, 101–134 (1964)

    Google Scholar 

  13. SPERNER, E., jr.: Ein Regularitätssatz für Systeme nichtlinearer elliptischer Differentialgleichungen. Math. Z.146, 57–68 (1976)

    Google Scholar 

  14. WIDMAN, K.-O.: Hölder continuity of solutions of elliptic systems, manusc. math.5, 299–308 (1971)

    Google Scholar 

  15. WIEGNER, M.: Über die Regularität schwacher Lösungen gewisser elliptischer Systeme. manusc. math.15, 365–384 (1975)

    Google Scholar 

  16. WIEGNER, M.: Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme. Math. Z.147, 21–28 (1976)

    Google Scholar 

  17. WIEGNER, M.: A-priori Schwanken für Lösungen gewisser elliptischer Systeme. manusc. math.18, 279–297 (1976)

    Google Scholar 

  18. WIEGNER, M.: Das Existenz- und Regularitätsproblem bei Systemen nichtlinearer elliptischer Differentialgleichungen, Habilitationsschrift, Bochum (1977)

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität, Beringstr. 6, 5300, Bonn 1

    Michael Struwe

Authors
  1. Michael Struwe
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft

Rights and permissions

Reprints and permissions

About this article

Cite this article

Struwe, M. On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems. Manuscripta Math 35, 125–145 (1981). https://doi.org/10.1007/BF01168452

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01168452

Keywords

Search

Navigation