Skip to main content
SpringerLink
Log in

Harmonic mappings with partially free boundary

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

The existence and regularity result of Hildebrandt — Kaul-Widman, concerning the Dirichlet problem for harmonic mappings between Riemannian manifolds, is extended to a mixed boundary value problem.

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. AGMON, S., The Lp-approach to the Dirichlet problem, Ann. Scuola Norm. Sup. Pisa13, 405–448 (1959)

    Google Scholar 

  2. DZIUK, G., Über die Stetigkeit teilweise freier Minimal-flächen, man. math.36, 241–251 (1981)

    Google Scholar 

  3. EELLS, J., and L. LEMAIRE, A report on harmonic maps, Bull. London Math. Soc.10, 1–68 (1978)

    Google Scholar 

  4. GRÜTER, M., and K.O. WIDMAN, The Green function for uniformly elliptic equations, man. math.37, 303–342 (1982)

    Google Scholar 

  5. GRÜTER, M., S. HILDEBRANDT and J.C.C. NITSCHE, On the boundary behaviour of minimal surfaces with a free boundary which are not minima of the area, man. math.35, 387–410 (1981)

    Google Scholar 

  6. HAMILTON, R.S., Harmonic maps of manifolds with boundary, Lecture Notes in Mathematics, No. 471, Springer, Berlin - Heidelberg - New York, 1975

    Google Scholar 

  7. HILDEBRANDT, S., Über das Randverhalten von Minimalflächen, Math. Ann.165, 1–18 (1966)

    Google Scholar 

  8. HILDEBRANDT, S., On the regularity of solutions of two-dimensional variational problems with obstructions, Comm. Pure Appl. Math.25, 479–496 (1972)

    Google Scholar 

  9. HILDEBRANDT, S., and H. KAUL, Two-dimensional variational problems with obstructions and Plateau's problem for H-surfaces in a Riemannian manifold, Comm. Pure Appl. Math.25, 187–223 (1972)

    Google Scholar 

  10. HILDEBRANDT, S., H. KAUL and K.O. WIDMAN, An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math.138, 1–16 (1977)

    Google Scholar 

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

    Google Scholar 

  12. JOST, J., Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen, man. math.32, 51–57 (1980)

    Google Scholar 

  13. LADYŽENSKAYA, O.A., et N.N. URAL'CEVA, Equations aux dérivées partielles de type elliptique, Dunod, Paris, 1968

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität Bonn, Beringstr. 4, D 5300, Bonn 1

    Alfred Baldes

Authors
  1. Alfred Baldes
    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

Baldes, A. Harmonic mappings with partially free boundary. Manuscripta Math 40, 255–275 (1982). https://doi.org/10.1007/BF01174879

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01174879

Keywords

Search

Navigation