Skip to main content
SpringerLink
Log in

A free boundary problem for capillary surfaces

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We prove existence and regularity of capillary surfaces between two parallel hyperplanes in ℝn. By geometrical arguments we also derive some properties of the minimizers of the functional related to the 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. M. Athanassenas: A variational problem for constant mean curvature surfaces with free boundary. Journ. Reine Angew. Math. 377 (1987), 97–107

    MATH  MathSciNet  Google Scholar 

  2. J.L. Barbosa, M. do Carmo: Stability of hypersufaces with constant mean curvature. Math. Zeitschrift, 185 (1984), 339–353

    Article  MATH  Google Scholar 

  3. Ch. Delaunay: Sur la surface de révolution dont la courbure moyenne est constante. Journ. de mathémathiques pures et appliquées 6 (1841), 309–320

    Google Scholar 

  4. M. Emmer: Esistenza, unicità e regolarità nelle superfici di equilibrio nei capillari. Ann. Univ. Ferrara, Ser. VIII 18 (1973), 79–94

    MathSciNet  Google Scholar 

  5. C. Gerhardt: Existence and regularity of capillary surfaces. Bollettino UMI (4) 10 (1974), 317–335

    MATH  MathSciNet  Google Scholar 

  6. E. De Giorgi: Sulla proprietà isoperimetrica dell' ipersfera, nella classi degli insiemi aventi frontiera orientata di misura finita. Atti Academia Nationale dei Lincei, Serie VIII, Vol. V (1958)

  7. E. De Giorgi, F. Colombini, L. Piccinini: Frontiere orientate di misura minima e questione collegate. Editrice Tecnico Scientifica, Pisa, 1972

    Google Scholar 

  8. E. Giusti: The equilibrium configuration of a liquid drop. Journ. Reine Angew. Math. 321 (1981), 53–63

    MATH  MathSciNet  Google Scholar 

  9. E. Giusti: Minimal surfaces and functions of bounded variation. Birkhäuser Verlag

  10. E. Gonzales: Sul problema della goccia appoggiata. Rend. Sem. Mat. Univ. Padova 55 (1976), 289–302

    MathSciNet  Google Scholar 

  11. E. Gonzales: Regolarità per il problema della goccia appoggiata. Rend. Sem. Mat. Univ. Padova 58 (1977), 25–33

    MathSciNet  Google Scholar 

  12. E. Gonzales, U. Massari, I. Tamanini: Existence and regularity for the problem of a pendent liquid drop. Pac. Journ. of Math. 88 No. 2 (1980), 399–420

    Google Scholar 

  13. E. Gonzales, U. Massari, I. Tamanini: On the regularity of boundaries of sets minimizing perimeter with a volume constraint. Indiana Univ. Math. Journ. 32 (1983), 25–37

    Article  Google Scholar 

  14. E. Gonzales, I. Tamanini: Convessità della goccia appoggiata. Rend. Sem. Mat. di Padova 58 (1977), 35–43

    Google Scholar 

  15. M. Grüter: Boundary regularity for solutions of a partitioning problem. Arch. Rat. Mech. Anal. 97 (1987), 261–270

    Article  MATH  Google Scholar 

  16. Wu-Yi Hsiang, Wen-Ci Yu: A generalization of a theorem of Delaunay. J. Diff. Geometry 16 (1981), 161–177

    MATH  MathSciNet  Google Scholar 

  17. S. Luckhaus: Partial boundary regularity for the parametric capillarity problem in arbitrary space dimension. SFB 123 Univ. Heidelberg (1987), Preprint No. 416

  18. U. Massari, M. Miranda: Minimal surfaces of codimension one. North-Holland, Notas de Matematica

  19. M. Miranda: Comportamento delle successioni convergenti di frontiere minimali. Rend. Sem. Mat. di Padova 38 (1967), 238–257

    MathSciNet  Google Scholar 

  20. I. Tamanini: Regularity results for almost minimal oriented hypersurfaces in ℝn. Quaderni del Dipartimento di Matematica dell' Università di Lecce, Q1, 1984

  21. J.E. Taylor: Boundary regularity for solutions to various capillarity and free boundary problems. Comm. Part. Diff. Equ. 2 (1977), 323–357

    MATH  Google Scholar 

  22. T.I. Vogel: Stability of a liquid drop trapped between two parallel planes. SIAM J. Appl. Math. 47 No. 3 (1987), 516–525

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik der Universität Augsburg, Universitätsstraße 8, 8900, Augsburg

    Maria Athanassenas

Authors
  1. Maria Athanassenas
    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

Athanassenas, M. A free boundary problem for capillary surfaces. Manuscripta Math 76, 5–19 (1992). https://doi.org/10.1007/BF02567743

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567743

Keywords

Search

Navigation