Skip to main content
Log in

An optimal regularity result for a class of quasilinear parabolic systems

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

The regularity results of Hildebrandt-Widman and Wiegner for elliptic systems are generalized to the parabolic case.

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

Access this article

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

Instant access to the full article PDF.

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. Giaguinta,M. - E.Giusti: On the regularity of the minima of variational integrals, to appear in Acta Math.

  3. Giaguinta,M. - S.HiIdebrandt: Estimation á-priori des solutions faibles de certains systèmes non linéaires elliptiques, Sémin.Goulanic — Meyer —Schwartz 198–1981, expos.XVII

  4. Giaquinta,M. - S.Hildebrandt: A priori estimates for harmonic mappings, to appear

  5. Giaquinta,M. - M.Struwe: On the partial regularity of non-linear parabolic systems, to appear

  6. Hildebrandt,S. - H.Kaul - K.-O.Widman: An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math.138,1–16 (1977)

    Google Scholar 

  7. Hildebrandt,S. - K.-O.Widman: On the Holder continuity of weak solutions of quasilinear elliptic systems of second order, Ann.Sc.Norm.Sup.Pisa, Ser.4,145–178 (1977)

    Google Scholar 

  8. Jost,J.: Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses, manusc.math.34, 17–25 (1981)

    Google Scholar 

  9. Kikuchi,H.: On the nonlinear equation of Eells-Sampson and a harmonic mapping with boundary condition, preprint

  10. Ladyshenskaya,O.A. - V.A.Solonnikov - N.N.Ural'ceva: Linear and quasilinear equations of parabolic type. Transi.Math.Monogr. 23, AMS, Providence, R.I. (1968)

    Google Scholar 

  11. Moser,J.: A Harnack inequality for parabolic differential equations, Comm. Pure Appl.Math. 17, 101–134 (1964), Errata, ibid.20, 231–236 (1967)

    Google Scholar 

  12. Sampson,J.H.: On the heat equation for harmonic maps, preprint

  13. Struwe,M.: On the Holder continuity of bounded weak solutions of quasilinear parabolic systems, manusc.math.35, 125–145 (1981)

    Google Scholar 

  14. Trudinger,N.S.: Pointwise estimates and quasilinear parabolic equations, Comm.Pure Appl.Math.21, 205–226 (1968)

    Google Scholar 

  15. v.Wahl,W.: Verhalten der Lösungen parabolischer Gleichungen für t→∞ mit Lösbarkeit im Gro⨿en, preprint

  16. Wiegner,M.: Das Existenz u. Regularitätsproblem bei Systemen nichtlinearer elliptischer Differentialgleichungen, Habilitationsschrift, Bochum (1977)

Download references

Author information

Authors and Affiliations

Authors

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

Giaquinta, M., Struwe, M. An optimal regularity result for a class of quasilinear parabolic systems. Manuscripta Math 36, 223–239 (1981). https://doi.org/10.1007/BF01170135

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01170135

Keywords

Navigation