DIRICHLET PROBLEM FOR MINIMAL SURFACE EQUATION ON UNBOUNDED-DOMAINS

This paper deals with the Dirichlet problem for the minimal surface equation in an unbounded domain of the plane. In the more general case of the prescribed mean curvature equation, the main theorem gives an estimate for the difference between two solutions in a neighbourhood of infinity. A general theorem of unicity of solution, and a maximum principle at infinity are deduced from it. A more specific study is done in the case of the minimal surface equation on some particular domains such as the strip or the half-plane.