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On the analyticity of generalized minimal surfaces

Published online by Cambridge University Press:  17 April 2009

Neil S. Trudinger
Affiliation:
University of Queensland, St Lucia, Queensland, and Stanford University, Stanford, California, USA.
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Abstract

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Strongly differentiable solutions of the minimal surface equation are shown to be classical solutions and consequently locally analytic. A global regularity result is also proved.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bers, Lipman; John, Fritz; Schechter, Martin, Partial differential equations. Proc. Summer Seminar, Boulder, Colorado, 1957; (Interscience [John Wiley & Sons], New York, London, Sydney, 1964).Google Scholar
[2]Bombieri, E., Miranda, E. De Giorgi e M., “Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche”, Arch. Rat. Mech. Anal. 32 (1969), 255267.CrossRefGoogle Scholar
[3]De Giorgi, Ennio, “Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari”, Mem. Accad. Sci. Torino, Cl. Sai. Fis. Mat. Natur. (3) 3 (1957), 2543.Google Scholar
[4]Jenkins, Howard and Serrin, James, “The Dirichlet problem for the minimal surface equation in higher dimensions”, J. reine angew. Math. 229 (1968), 170187.Google Scholar
[5]Ladyzhenskaya, Olga A. and Ural'tseva, Nina N., Linear and quasilinear elliptic equations, (Russian: Izd. Nauka, Moscow, 1964; English transl.: Academic Press, New York, London, 1968).Google Scholar
[6]Nitsche, Johannes C. C., Private communication, 1970.Google Scholar
[7]Serrin, James, “Local behavior of solutions of quasilinear equations”, Acta Math. 111 (1964), 247302.CrossRefGoogle Scholar