We solve the Dirichlet problem for strictly convex, spacelike hypersurfaces of prescribed Weingarten curvature under the main assumption that there exists an upper barrier. We consider curvature functions that correspond in general to fully nonlinear elliptic partial differential equations which are not uniformly elliptic.
A shortened version of this paper has appeared in "Mathematische Zeitschrift". Springer-Verlag is the copyright holder of this article. The original publication is available on LINK at http://link.springer.de, more precisely, see http://dx.doi.org/10.1007/s002090100312.