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How a minimal surface leaves an obstacle

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References

  1. Bers, L., John, F. &Schechter, M.,Partial Differential Equations. Interscience, New York, 1962.

    Google Scholar 

  2. Caratheodory, C.,Conformal Representation. Cambridge University Press, London, 1932.

    MATH  Google Scholar 

  3. Courant, R. &Hilbert, D.,Methods of Mathematical Physics, vol. II, Partial Differential Equations, Interscience, New York, 1962 (esp. p. 350).

    MATH  Google Scholar 

  4. Giaquinta, M. &Pepe, L., Esistenza e regolarità per il problema dell'area minima con ostacoli inn variabili.Ann. Scuola Norm, Sup. Pisa, 25 (1971), 481–506.

    MATH  MathSciNet  Google Scholar 

  5. Hartman, P. &Wintner, A., On the local behavior of non parabolic partial differential equations.Amer. J. Math., 85 (1953), 449–476.

    Article  MathSciNet  Google Scholar 

  6. Kinderlehrer, D., The coincidence set of solutions of certain variational inequalities.Arch. Rational Mech. Anal., 40 (1971), 231–250.

    Article  MATH  MathSciNet  Google Scholar 

  7. Kinderlehrer, D., The regularity of the solution to a certain variational inequality.Proc. Symp. Pure and Appl. Math., 23 AMS, Providence RI.

  8. Kinderlehrer, D., How a minimal surface leaves an obstacle. To appear inBull. Amer. Math. Soc., 78 (1972).

  9. Lewy, H., On the boundary behavior of minimal surfaces.Proc. Nat. Acad. Sci. USA, 37 (1951), 103–110.

    Article  MATH  MathSciNet  Google Scholar 

  10. — On minimal surfaces with partly free boundary.Comm. Pure Appl. Math., 4 (1951), 1–13.

    MathSciNet  Google Scholar 

  11. Lewy, H. &Stampacchia, G., On the regularity of the solution to a variational inequality.Comm. Pure Appl. Math., 22 (1969), 153–188.

    MATH  MathSciNet  Google Scholar 

  12. — On the existence and smoothness of solutions of some noncoercive variational inequalitiesArch. Rational Mech. Anal., 41 (1971), 141–253.

    Article  MathSciNet  Google Scholar 

  13. Nitsche, J. C. C., The boundary behavior of minimal surfaces.Invent. Math., 8 (1969), 313–333.

    Article  MATH  MathSciNet  Google Scholar 

  14. —, On new results in the theory of minimal surfaces.Bull. Amer. Math. Soc., 71 (1965) 195–270.

    Article  MATH  MathSciNet  Google Scholar 

  15. Rado, T.,On the problem of Plateau, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1933.

    Google Scholar 

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This research was partially supported by contract AFOSR 71-2098 and a Borsa di Studio del C.N.R. (1971–1972).

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Kinderlehrer, D. How a minimal surface leaves an obstacle. Acta Math. 130, 221–242 (1973). https://doi.org/10.1007/BF02392266

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  • DOI: https://doi.org/10.1007/BF02392266

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