Abstract
Extending the variational approach to Plateau’s problem developed in [6], we show that similar results can be obtained for surfaces normalized by a 3-point condition. Moreover, we supply further details for the regularity results in [6].
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References
R. Courant: Dirichle’s principle, conformai mapping and minimal surfaces, New York, Interscience, 1950.
K. Deimling: Nonlinear functional analysis, Springer, Berlin, etc., 1985.
S. Hildebrandt: “Boundary behavior of minimal surfaces”, Arch. Rat. Mech. Anal. 35 (1969), 47–82.
C. Imbusch: Eine Anwendung des Mountain-Pass-Lemmas auf den Fragenkreis des Plateauschen Problems und eine Alternative zur Drei-Punkte-Bedingung, Diplomarbeit, Bonn, Februar 1997.
J.-L. Lions, E. Magenes: Non-homogeneous boundary value problems and applications I, Springer Grundlehren 181, Berlin-Heidelberg-New York, 1972.
M. Struwe: “Plateau’s problem and the calculus of variations”, Mathematical Notes 35, Princeton, New Jersey, 1988.
K.O. Widman: “Hölder continuity of solutions of elliptic systems”, Manusc. Math. 5 (1971), 299–308.
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© 1999 Springer Basel AG
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Imbusch, C., Struwe, M. (1999). Variational Principles for Minimal Surfaces. In: Escher, J., Simonett, G. (eds) Topics in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 35. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8765-6_19
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DOI: https://doi.org/10.1007/978-3-0348-8765-6_19
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9764-8
Online ISBN: 978-3-0348-8765-6
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