An exterior boundary value problem in Minkowski space

In three-dimensional Lorentz-Minkowski space L-3, we consider a spacelike plane Pi and a round disc Q over H. In this article we seek the shapes of unbounded surfaces whose boundary is partial derivative Omega and its mean curvature is a linear function of the distance to Pi. These surfaces, called stationary surfaces, are solutions of a variational problem and governed by the young-Laplace equation. In this sense, they generalize the surfaces with constant mean curvature in L-3. We shall describe all axially symmetric unbounded stationary surfaces with special attention in the case that the surface is asymptotic to Pi at the infinity. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.