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THE DIRICHLET PROBLEM FOR THE MINIMAL SURFACES EQUATION AND THE PLATEAU PROBLEM AT INFINITY

Published online by Cambridge University Press:  01 July 2004

Laurent Mazet
Laurent Mazet
Affiliation:
Laboratoire Emile Picard, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse, France (mazet@picard.ups-tlse.fr)
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Abstract

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In this paper, we shall study the Dirichlet problem for the minimal surfaces equation. We prove some results about the boundary behaviour of a solution of this problem. We describe the behaviour of a non-converging sequence of solutions in term of lines of divergence in the domain. Using this second result, we build some solutions of the Dirichlet problem on unbounded domain. We then give a new proof of the result of Cosín and Ros concerning the Plateau problem at infinity for horizontal ends.

AMS 2000 Mathematics subject classification: Primary 53A10

Keywords

minimal surfaceDirichlet problemboundary behaviour
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 3 , Issue 3 , July 2004 , pp. 397 - 420
Copyright
2004 Cambridge University Press