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Variational Principles for Minimal Surfaces

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Topics in Nonlinear Analysis

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

  1. R. Courant: Dirichle’s principle, conformai mapping and minimal surfaces, New York, Interscience, 1950.

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  5. J.-L. Lions, E. Magenes: Non-homogeneous boundary value problems and applications I, Springer Grundlehren 181, Berlin-Heidelberg-New York, 1972.

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  6. M. Struwe: “Plateau’s problem and the calculus of variations”, Mathematical Notes 35, Princeton, New Jersey, 1988.

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  7. 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

  • eBook Packages: Springer Book Archive

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