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On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area

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Abstract

The well known boundary regularity results of H. Lewy and W. Jäger for area minimizing minimal surfaces with a free boundary are shown to be true also for minimal surfaces which are only stationary points of the Dirichlet integral with respect to a given boundary configuration.

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Bibliography

  1. COURANT, R.: Dirichlet's principle, conformai mapping, and minimal surfaces. Interscience, New York 1950

    Google Scholar 

  2. DZIUK, G.: On the boundary behavior of partially free minimal surfaces, manuscripta math.35, 105–123 (1981)

    Google Scholar 

  3. GRÜTER, M.: Über die Regularität schwacher Lösungen des Systems Δx=2H(x)xu ∧ xv, Dissertation, Düsseldorf 1979

    Google Scholar 

  4. GRÜTER, M.: Regularity of weak H-surfaces, to appear

  5. HILDEBRANDT, S. and WIDMAN, K.-O.: Some regularity results for quasilinear elliptic systems of second order, Math. Z.142, 67–86 (1975)

    Google Scholar 

  6. HILDEBRANDT, S. and NITSCHE, J.C.C.: Minimal surfaces with free boundaries, Acta Math.143, 251–272 (1979)

    Google Scholar 

  7. HILDEBRANDT, S. and NITSCHE, J.C.C.: A uniqueness theorem for surfaces of least area with partially free boundaries on obstacles, to appear in Archive for Rat. Mech. Analysis

  8. HILDEBRANDT, S. and NITSCHE, J.C.C.: Optimal boundary regularity for minimal surfaces with a free boundary, manuscripta math.33, 357–364 (1981)

    Google Scholar 

  9. JÄGER, W.: Behavior of minimal surfaces with free boundaries, Comm. Pure Appl. Math.23, 803–818 (1970)

    Google Scholar 

  10. LEWY, H.: On minimal surfaces with partially free boundary, Comm. Pure Appl. Math.4, 1–13 (1951)

    Google Scholar 

  11. MORREY, C.B.: Multiple integrals in the calculus of variations, Springer, Berlin-Heidelberg-New York 1966

    Google Scholar 

  12. NITSCHE, J.C.C.: Vorlesungen über Minimalflächen, Springer, Berlin-Heidelberg-New York 1975

    Google Scholar 

  13. SCHWARZ, H.A.: Gesammelte Mathematische Abhandlungen, Erster Band, Springer, Berlin 1890

    Google Scholar 

  14. WIDMAN, K.-O: Holder continuity of solutions of elliptic systems, manuscripta math.5, 299–308 (1971)

    Google Scholar 

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Authors and Affiliations

  1. Math. Institut, Univ. Düsseldorf, Universitätsstr. 1, D-4000, Düsseldorf

    Michael Grüter

  2. Math. Institut, Universität Bonn, Wegelerstr. 10, D-5300, Bonn 1

    Stefan Hildebrandt

  3. School of Mathematics, Univ. of Minnesota, 127 Vincent Hall, 55455, Minneapolis, MN, USA

    Johannes C. C. Nitsche

Authors
  1. Michael Grüter
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  2. Stefan Hildebrandt
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  3. Johannes C. C. Nitsche
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Grüter, M., Hildebrandt, S. & Nitsche, J.C.C. On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area. Manuscripta Math 35, 387–410 (1981). https://doi.org/10.1007/BF01263271

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  • DOI: https://doi.org/10.1007/BF01263271

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