A liouville-type theorem for some weingarten hypersurfaces

We consider the entire graph G of a globally Lipschitz continuous function u over R ^N with N ≥ 2, and consider a class of some Weingarten hy- persurfaces in R ^N+1. It is shown that, if u solves in the viscosity sense in R ^N the fully nonlinear elliptic equation of a Weingarten hypersurface belonging to this class, then u is an affine function and G is a hyperplane. This result is regarded as a Liouville-type theorem for a class of fully nonlinear elliptic equa- tions. The special case for some Monge-Ampère-type equation is related to the previous result of Magnanini and Sakaguchi which gave some characterizations of the hyperplane by making use of stationary isothermic surfaces.