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Infinite boundary value problems for surfaces of constant mean curvature

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Bibliography

  1. Alexandrov, A. D., Uniqueness theorems for surfaces in the large. Translated in Am. Math. Soc. Translations (Series 2) 21, 341–403, 412–416 (1956–58).

    Google Scholar 

  2. Bombieri, E., E. de Giorgi, & M. Miranda, Una maggiorazione a priori relativa alle ipercurfici minimali non parametriche. Arch. Rational Mech. Anal. 32 (1969).

  3. Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. II. Interscience, New York 1962.

    Google Scholar 

  4. Delaunay, Ch., Sur la surface de revolution dont la courbure moyenne est constante. J. Math. Pure Appl. 6, 309–315 (1841).

    Google Scholar 

  5. Finn, R., Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature. J. d'Anal. Math. 14, 139–160 (1965).

    Google Scholar 

  6. Finn, R., New estimates for equations of minimal surface type. Arch. Rational Mech. Anal. 14, 337–375 (1963).

    Google Scholar 

  7. Finn, R., & R. Osserman, On the Gauss curvature of nonparametric minimal surfaces. J. d'Anal. Math. 12, 351–364 (1964).

    Google Scholar 

  8. Heinz, E., Über die Lösungen der Minimalflächengleichung. Nach. Akad. Wiss. Göttingen Math., Phys. Kl. II p. 51–56 (1952).

  9. Hopf, E., Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus. Sber. Preuss. Akad. Wiss. 19, 147–152 (1927).

    Google Scholar 

  10. Jenkins, H., & J. Serrin, The Dirichlet problem for the minimal surface equation in higher dimensions. J. Reine Angew. Math. 229, 170–189 (1968).

    Google Scholar 

  11. Jenkins, H., & J. Serrin, Variational problems of minimal surface type II: boundary value problems for the minimal surface equation. Arch. Rational Mech. Anal. 21, 321–342 (1965–66).

    Google Scholar 

  12. Jenkins, H., & J. Serrin, Variational problems of minimal surface III. The Dirichlet problem with infinite data. Arch. Rational Mech. Anal. 29, 304–322 (1968).

    Google Scholar 

  13. Ladyzhenskaya, O. A., & N. N. Ural'tseva, Local estimates for the gradients of solutions of non-uniformly elliptic and parabolic equations. Comm. Pure Appl. Math. 23, 677–703 (1970).

    Google Scholar 

  14. Nirenberg, L., On nonlinear elliptic partial differential equations and Hölder continuity. Comm. Pure Appl. Math. 6, 103–156 (1952).

    Google Scholar 

  15. Nitsche, J. C. C., On new results in the theory of minimal surfaces. Bull. Amer. Math. Soc. 71, 195–270 (1965).

    Google Scholar 

  16. Nitsche, J. C. C., Über ein verallgemeinertes Dirichletsches Problem für die Minimalflächengleichung und hebbare Unstetigkeiten ihrer Lösungen. Math. Ann. 158, 203–214 (1965).

    Google Scholar 

  17. Osserman, R., A survey of Minimal Surfaces. New York: Van Nostrand Reinhold 1969.

    Google Scholar 

  18. Radó, T., On the Problem of Plateau. Berlin: Springer 1933.

    Google Scholar 

  19. Serrin, J., The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Roy. Soc. London A 264, 413–496 (1969).

    Google Scholar 

  20. Serrin, J., The Dirichlet problem for surfaces of constant mean curvature. Proc. London Math. Soc. 21, 361–384 (1970).

    Google Scholar 

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Communicated by J. Serrin

This research was supported in part by National Science Foundation Grant GU-2582.

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Spruck, J. Infinite boundary value problems for surfaces of constant mean curvature. Arch. Rational Mech. Anal. 49, 1–31 (1972). https://doi.org/10.1007/BF00281471

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