Skip to main content
Log in

Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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.

Literatur

  1. Courant, R.: The existence of minimal surfaces of given topological structure under prescribed boundary conditions. Acta Math.72, 51–98 (1940).

    Google Scholar 

  2. —: On Plateau's problem with free boundaries. Proc. Nat. Acad. Sci. U.S.A.31, 242–246 (1945).

    Google Scholar 

  3. —: Dirichlet's principle, conformal mapping, and minimal surfaces. New York: Interscience Publ. 1950.

    Google Scholar 

  4. — Davids, N.: Minimal surfaces spanning closed manifolds. Proc. Nat. Acad. Sci. U.S.A.26, 194–199 (1940).

    Google Scholar 

  5. Davids, N.: Minimal surfaces spanning closed manifolds and having prescribed topological position. Amer. J. Math.64, 348–362 (1942).

    Google Scholar 

  6. Goldhorn, K.H.: Dissertation. Mainz 1971.

  7. Harth, F.P.: Minimalflächen in Riemannschen Mannigfaltigkeiten mit freiem Rand. Dissertation. Mainz 1970.

  8. Hildebrandt, S.: Über Minimalflächen mit freiem Rand. Math. Z.95, 1–19 (1967).

    Google Scholar 

  9. —: Boundary behavior of minimal surfaces. Arch. Rat. Mech. Analysis35, 47–82 (1969).

    Google Scholar 

  10. —: Über Flächen konstanter mittlerer Krümmung. Math. Z.112, 107–144 (1969).

    Google Scholar 

  11. Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. II. Freie Ränder. Arch. Rat. Mech. Analysis. Erscheint demnächst.

  12. Hildebrandt, S., Jäger, W.: On the regularity of surfaces with prescribed mean curvature at a free boundary. Math. Z. Erscheint demnächst.

  13. Jäger, W.: The behavior of minimal surfaces with free boundaries. Commun. Pure Appl. Math. Erscheint demnächst.

  14. Lewy, H.: On minimal surfaces with partially free boundary. Commun. Pure Appl. Math.4, 1–13 (1951).

    Google Scholar 

  15. Morrey, C. B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Soc.43, 126–166 (1938).

    Google Scholar 

  16. —: Multiple integral problems in the calculus of variations and related topics. Univ. California Publ. Math., New Ser.1, 1–130 (1943).

    Google Scholar 

  17. —: The problem of Plateau on a Riemannian manifold. Ann. of Math.49, 807–851 (1948).

    Google Scholar 

  18. —: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  19. Nitsche, J. C. C.: The behavior of minimal surfaces with free boundaries. Remark on a paper by W. Jäger. Manuskript.

  20. Warschawski, S.: On the differentiability at the boundary in conformal mapping. Proc. Amer. Math. Soc.12, 614–620 (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goldhorn, K., Hildebrandt, S. Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen. Math Z 118, 241–253 (1970). https://doi.org/10.1007/BF01109861

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01109861

Navigation