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On the boundary behaviour of partially free minimal surfaces

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Abstract

Let S be a smooth surface in Euclidean 3-space and let C be a smooth curve having its end points on S. Consider a surface x, bounded by the configuration <S,C>, which minimizes Dirichlet's integral. We describe the local behaviour of x at the points where the arc C meets the boundary surface S.

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Literature

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

    Google Scholar 

  2. DZIUK, G.: Das Verhalten von Lösungen semilinearer elliptischer Systeme an Ecken eines Gebietes. Math. Z.159, 89–100 (1978)

    Google Scholar 

  3. DZIUK, G.: Ober quasilineare elliptische Systeme mit isothermen Parametern an Ecken der Randkurve. To appear in Analysis (1981)

  4. GOLDHORN, K. H.; HILDEBRANDT, S.: Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen. Math. Z.118, 241–253 (1970)

    Google Scholar 

  5. HEINZ, E.: Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern. Math. Z.113, 99–105 (1970)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  8. NITSCHE, J. C. C.: Minimal surfaces with partially free boundary. Least area property and Holder continuity for boundaries satisfying a chord-arc condition. Arch. Rat. Mech. Anal.39, 131–145 (1970)

    Google Scholar 

  9. NITSCHE, J. C. C.: Vorlesungen über Minimalflächen. Grundlehren der mathematischen Wissenschaften 199, Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

  10. NITSCHE, J. C. C.: The regularity of the trace for minimal surfaces. Annali Scuola Norm. Sup. Pisa, Ser. IV,3, 139–155 (1976)

    Google Scholar 

  11. TAYLOR, J. E.: Boundary regularity for solutions to various capillarity and free boundary problems. Comm. P. D. E.2 (4), 323–357 (1977)

    Google Scholar 

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  1. Institut für Mathematik, RWTH, Templergraben 55, D-5100, Aachen, BRD

    Gerhard Dziuk

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  1. Gerhard Dziuk
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Dziuk, G. On the boundary behaviour of partially free minimal surfaces. Manuscripta Math 35, 105–123 (1981). https://doi.org/10.1007/BF01168451

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  • DOI: https://doi.org/10.1007/BF01168451

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