Skip to main content
SpringerLink
Log in

Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

This paper is concerned with the initial — boundary value problem for the parabolic system associated with harmonic mappings of Riemannian manifolds. We prove the existence of solutions u(x,t) for all time and verify that u(·,t) tends to a harmonic mapping u∞(·), as t→∞, which assumes the prescribed boundary values. The assumption on the Riemannian manifolds are the same as in the elliptic case.

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

Literatur

  1. Eells,J., und J.H.Sampson, “Harmonic Mappings of Riemannian Manifolds”, Amer.J.Math.86, 109–160 (1964)

    Google Scholar 

  2. Hamilton, R., “Harmonic Maps of Manifolds with Boundary”, Springer Lecture Notes 471, Berlin, Heidelberg, New York 1975

  3. Hartman,P., “On Homotopic Harmonic Maps”, Can.J.Math.19, 673–687 (1967)

    Google Scholar 

  4. Hildebrandt,S., J.Jost und K.-O.Widman, “Harmonic Mappings and Minimal Submanifolds”, erscheint in Inv.math.

  5. Hildebrandt,S., H.Kaul und K.-O.Widman, “Harmonic Mappings into Riemannian Manifolds with Non-positive Sectional Curvature”, Math.Scand.37, 257–263 (1975)

    Google Scholar 

  6. dies., “Dirichlet's Boundary Value Problem for Harmonic Mappings of Riemannian Manifolds”, MZ147, 225–236 (1976)

    Google Scholar 

  7. dies., “An Existence Theorem for Harmonic Mappings of Riemannian Manifolds”, Acta Math.138, 1–16 (1977)

    Google Scholar 

  8. Hildebrandt,S. und K.-O.Widman, “On the Hölder Continuity of Weak Solutions of Quasilinear Elliptic Systems of Second Order”, Annali Sc.N.Pisa(IV)4, 145–178 (1977)

    Google Scholar 

  9. Jäger,W. und H.Kaul, “Uniqueness and Stability of Harmonic Maps and their Jacobi Fields”, man.math.28, 269–291 (1979)

    Google Scholar 

  10. Jost,J., “Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen”, erscheint in man.math.

  11. Ladyženskaja,O.A. und N.N.Ural'ceva, “Équations aux dérivées partiells de type elliptique”, Dunod, Paris 1968

    Google Scholar 

  12. v.Wahl,W., “Existenzsätze für nichtlineare elliptische Systeme”, Nachr.Akad.Wiss.Gött.Nr.3 (1978)

  13. v.Wahl,W., “Verhalten der Lösungen parabolischer Gleichungen für t→∞ und Lösbarkeit im Großen”, Vortrag, gehalten am 17.7.80 in Oberwolfach

Download references

Author information

Authors and Affiliations

  1. Math. Inst. der Univers. Bonn, Beringstr. 4, D - 5300, Bonn 1

    Jürgen Jost

Authors
  1. Jürgen Jost
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jost, J. Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta Math 34, 17–25 (1981). https://doi.org/10.1007/BF01168706

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01168706

Search

Navigation