The Dirichlet problem for minimal surfaces equation and Plateau problem at infinity

2003/03/17 by Laurent Mazet, Mazet, Laurent
Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.math/0303199

30 pages, 4 figures

arxiv created 2003/03/17 · arxiv updated 2009/11/30

Abstract

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 C. Cos'ın and A. Ros concerning the Plateau problem at infinity for horizontal ends.

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