THE DIRICHLET PROBLEM FOR THE MINIMAL SURFACES EQUATION AND THE PLATEAU PROBLEM AT INFINITY
Laurent Mazet · Journal of the Institute of Mathematics of Jussieu · 2004
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