Infinite boundary value problems for surfaces of constant mean curvature. (English) Zbl 0263.53008

Spruck, Joel

Arch. Ration. Mech. Anal. 49, 1-31 (1972).

MSC:

53A05	Surfaces in Euclidean and related spaces
35J60	Nonlinear elliptic equations
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

References:

[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).
[2]	Bombieri, E., E. de Giorgi, & M. Miranda, Una maggiorazione a priori relativa alle ipercurfici minimali non parametriche. Arch. Rational Mech. Anal. 32 (1969). · Zbl 0184.32803
[3]	Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. II. Interscience, New York 1962. · Zbl 0099.29504
[4]	Delaunay, Ch., Sur la surface de revolution dont la courbure moyenne est constante. J. Math. Pure Appl. 6, 309-315 (1841).
[5]	Finn, R., Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature. J. d’Anal. Math. 14, 139-160 (1965). · Zbl 0163.34604 · doi:10.1007/BF02806384
[6]	Finn, R., New estimates for equations of minimal surface type. Arch. Rational Mech. Anal. 14, 337-375 (1963). · Zbl 0133.04601 · doi:10.1007/BF00250712
[7]	Finn, R., & R. Osserman, On the Gauss curvature of nonparametric minimal surfaces. J. d’Anal. Math. 12, 351-364 (1964). · Zbl 0122.16404 · doi:10.1007/BF02807440
[8]	Heinz, E., Über die Lösungen der Minimalflächengleichung. Nach. Akad. Wiss. Göttingen Math., Phys. Kl. II p. 51-56 (1952). · Zbl 0048.15401
[9]	Hopf, E., Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus. Sber. Preuss. Akad. Wiss. 19, 147-152 (1927). · JFM 53.0454.02
[10]	Jenkins, H., & J. Serrin, The Dirichlet problem for the minimal surface equation in higher dimensions. J. Reine Angew. Math. 229, 170-189 (1968). · Zbl 0159.40204 · doi:10.1515/crll.1968.229.170
[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). · Zbl 0171.08301
[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). · Zbl 0167.11403 · doi:10.1007/BF00276730
[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). · Zbl 0193.07202 · doi:10.1002/cpa.3160230409
[14]	Nirenberg, L., On nonlinear elliptic partial differential equations and Hölder continuity. Comm. Pure Appl. Math. 6, 103-156 (1952). · Zbl 0050.09801 · doi:10.1002/cpa.3160060105
[15]	Nitsche, J. C. C., On new results in the theory of minimal surfaces. Bull. Amer. Math. Soc. 71, 195-270 (1965). · Zbl 0135.21701 · doi:10.1090/S0002-9904-1965-11276-9
[16]	Nitsche, J. C. C., Über ein verallgemeinertes Dirichletsches Problem für die Minimalflächengleichung und hebbare Unstetigkeiten ihrer Lösungen. Math. Ann. 158, 203-214 (1965). · Zbl 0141.09601 · doi:10.1007/BF01360040
[17]	Osserman, R., A survey of Minimal Surfaces. New York: Van Nostrand Reinhold 1969. · Zbl 0209.52901
[18]	Radó, T., On the Problem of Plateau. Berlin: Springer 1933. · JFM 59.1341.01
[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). · Zbl 0181.38003 · doi:10.1098/rsta.1969.0033
[20]	Serrin, J., The Dirichlet problem for surfaces of constant mean curvature. Proc. London Math. Soc. 21, 361-384 (1970). · Zbl 0199.16604 · doi:10.1112/plms/s3-21.2.361