Advertisement

Mathematische Zeitschrift

, Volume 185, Issue 4, pp 449–464 | Cite as

Capillary surfaces in negative gravitational fields

  • Gerhard Huisken
Article

Keywords

Gravitational Field Capillary Surface 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen, J.: On the existence of capillary surfaces in the absence of gravity. Pacific J. Math.88, 323–361 (1980)Google Scholar
  2. 2.
    Concus, P., Finn, R.: On capillary free surfaces in a gravitational field. Acta Math.132, 207–223 (1974)Google Scholar
  3. 3.
    Finn, R.: A subsidiary variational problem and existence criteria for capillary surfaces. PreprintGoogle Scholar
  4. 4.
    Gerhardt, C.: Global regularity of the solutions to the capillarity problem. Ann. Scuola Norm. Sup. Pisa Ser. (4)3, 157–175 (1976)Google Scholar
  5. 5.
    Gerhardt, C.: On the capillarity problem with constant volume. Ann. Scuola Norm. Sup. Pisa Ser. (4)2, 304–320 (1975)Google Scholar
  6. 6.
    Gerhardt, C.: Existence and regularity of capillary surfaces. Boll. Un. Mat. Ital.10, 317–335 (1974)Google Scholar
  7. 7.
    Giaquinta, M.: On the Dirichlet problem for surfaces of prescribed mean curvature, Manuscripta Math.12, 73–86 (1974)Google Scholar
  8. 8.
    Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Grundl. Math. Wiss.224. Berlin-Heidelberg-New York: Springer 1977Google Scholar
  9. 9.
    Giusti, E.: Boundary value problems for non-parametric surfaces of prescribed mean curvature. Ann. Scuola Norm. Sup. Pisa Ser. (4)3, 501–548 (1976)Google Scholar
  10. 10.
    Giusti, E.: On the equation of surfaces of prescribed mean curvature. Invent. Math.46, 111–137 (1978)Google Scholar
  11. 11.
    Giusti, E.: The pendent water drop. A direct approach. Boll. Un. Mat. Ital.17, 458–465 (1980)Google Scholar
  12. 12.
    Gonzales, E.: Sul problema della goccia appoggiata. Rend. Sem. Mat. Univ. Padova55, 289–302 (1976)Google Scholar
  13. 13.
    Huisken, G.: Capillary surfaces over obstacles. To appear in Pacific J. Math.Google Scholar
  14. 14.
    Massari, U., Pepe, L.: Su di una formulazione variazionale del problema dei capillari in assenza di gravitá. Ann. Univ. Ferrara Sez. VIII20, 33–42 (1974)Google Scholar
  15. 15.
    Michael, J.H., Simon, L.M.: Sobolev and mean value inequalities on generalized submanifolds of ℝn. Comm. Pure Appl. Math.26, 361–379 (1973)Google Scholar
  16. 16.
    Serrin, J.: The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Philos. Trans. Roy. Soc. London Ser. A264, 313–496 (1969)Google Scholar
  17. 17.
    Stampacchia, G.: Equations elliptiques du second ordre à coefficients discontinus. Montréal: Les Presses de l'Université 1966Google Scholar
  18. 18.
    Ural'ceva, N.N.: The solvability of the capillarity problem. Vestnik Leningrad Univ. Mat. Meh. Astronom.4, 54–64 (1973) [Russian]Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Gerhard Huisken
    • 1
  1. 1.Institut für Angewandte MathematikRuprecht-Karls-UniversitätHeidelbergGermany

Personalised recommendations