How a minimal surface leaves an obstacle. (English) Zbl 0268.49050


49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
35J99 Elliptic equations and elliptic systems
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[1] Bers, L., John, F. &Schechter, M.,Partial Differential Equations. Interscience, New York, 1962.
[2] Caratheodory, C.,Conformal Representation. Cambridge University Press, London, 1932.
[3] Courant, R. &Hilbert, D.,Methods of Mathematical Physics, vol. II, Partial Differential Equations, Interscience, New York, 1962 (esp. p. 350). · Zbl 0099.29504
[4] Giaquinta, M. &Pepe, L., Esistenza e regolarit√† per il problema dell’area minima con ostacoli inn variabili.Ann. Scuola Norm, Sup. Pisa, 25 (1971), 481–506. · Zbl 0283.49032
[5] Hartman, P. &Wintner, A., On the local behavior of non parabolic partial differential equations.Amer. J. Math., 85 (1953), 449–476. · Zbl 0052.32201
[6] Kinderlehrer, D., The coincidence set of solutions of certain variational inequalities.Arch. Rational Mech. Anal., 40 (1971), 231–250. · Zbl 0219.49014
[7] Kinderlehrer, D., The regularity of the solution to a certain variational inequality.Proc. Symp. Pure and Appl. Math., 23 AMS, Providence RI. · Zbl 0273.35027
[8] Kinderlehrer, D., How a minimal surface leaves an obstacle. To appear inBull. Amer. Math. Soc., 78 (1972). · Zbl 0262.53003
[9] Lewy, H., On the boundary behavior of minimal surfaces.Proc. Nat. Acad. Sci. USA, 37 (1951), 103–110. · Zbl 0042.15702
[10] – On minimal surfaces with partly free boundary.Comm. Pure Appl. Math., 4 (1951), 1–13.
[11] Lewy, H. &Stampacchia, G., On the regularity of the solution to a variational inequality.Comm. Pure Appl. Math., 22 (1969), 153–188. · Zbl 0167.11501
[12] – On the existence and smoothness of solutions of some noncoercive variational inequalitiesArch. Rational Mech. Anal., 41 (1971), 141–253. · Zbl 0237.49005
[13] Nitsche, J. C. C., The boundary behavior of minimal surfaces.Invent. Math., 8 (1969), 313–333. · Zbl 0195.23101
[14] –, On new results in the theory of minimal surfaces.Bull. Amer. Math. Soc., 71 (1965) 195–270. · Zbl 0135.21701
[15] Rado, T.,On the problem of Plateau, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1933. · Zbl 0007.11804
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