Skip to main content

Some results on minimal surfaces with free boundaries

Part of the Lecture Notes in Mathematics book series (LNM,volume 1107)

Keywords

  • Free Boundary
  • Minimal Surface
  • Branch Point
  • Obstacle Problem
  • Manuscripta Math

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. R. COURANT: Dirichlet's principle, conformal mapping, and minimal surfaces. Interscience, New York 1950.

    MATH  Google Scholar 

  3. G. DZIUK: Über die Stetigkeit teilweise freier Minimalflächen. Manuscripta math. 36, 241–251 (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. J. FREHSE: Un problème variationel bidimensionel possédant des extremales bornées et dicontinues. C.R. Acad. Scienc. Paris.

    Google Scholar 

  5. J.D. GERGONNE: Questions proposées. Ann. Math. Pure Appl. 7, 68, 99–100, 156 (1816).

    Google Scholar 

  6. M. GRÜTER: Über die Regularität schwacher Lösungen des Systems Δx=2H(x)xuΓxv. Dissertation, Düsseldorf 1979.

    Google Scholar 

  7. M. GRÜTER: Regularity of weak H-surfaces. Journal für die Reine Angew. Math. 329, 1–15 (1981).

    MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. S. HILDEBRANDT, and J.C.C. NITSCHE: Minimal surfaces with free boundaries. Acta Math. 143, 251–272 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. S. HILDEBRANDT, and J.C.C. NITSCHE: A uniqueness theorem for surfaces of least area with partially free boundaries on obstacles. To appear in Archive for Rat. Mech. Analysis.

    Google Scholar 

  12. S. HILDEBRANDT, and J.C.C. NITSCHE: Optimal boundary regularity for minimal surfaces with a free boundary. Manuscripta math. 33, 357–364 (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. S. HILDEBRANDT, and J.C.C. NITSCHE: Geometric properties of minimal surfaces with free boundaries. Preprint (1982).

    Google Scholar 

  14. W. JÄGER: Behavior of minimal surfaces with free boundaries. Comm. Pure Appl. Math. 23, 803–818 (1970).

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. H. LEWY: On minimal surfaces with partially free boundary. Comm. Pure Appl. Math. 4, 1–13 (1951).

    CrossRef  MathSciNet  Google Scholar 

  16. C.B. MORREY: Multiple integrals in the calculus of variations. Springer, Berlin-Heidelberg-New York 1966.

    MATH  Google Scholar 

  17. J.C.C. NITSCHE: Vorlesungen über Minimalflächen. Springer, Berlin-Heidelberg-New York 1975.

    CrossRef  MATH  Google Scholar 

  18. H.A. SCHWARZ: Fortgesetzte Untersuchungen über spezielle Minimalflächen. Monatsberichte der Königlichen Akad. Wiss. Berlin, 3–27 (1872). Gesammelte Math. Abhandlungen I, 126–148 (1890).

    Google Scholar 

  19. J.E. TAYLOR: The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Annals of Math. 103, 489–539 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. J.E. TAYLOR: Boundary regularity for various capillarity and boundary problems. Comm. P.D.E. 2, 323–357 (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Hildebrandt, S. (1984). Some results on minimal surfaces with free boundaries. In: Vinti, C. (eds) Nonlinear Analysis and Optimization. Lecture Notes in Mathematics, vol 1107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101497

Download citation

  • DOI: https://doi.org/10.1007/BFb0101497

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13903-4

  • Online ISBN: 978-3-540-39123-4

  • eBook Packages: Springer Book Archive