科研之友
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摘要
We consider the entire graph J of a globally Lipschitz continuous function u over R-N with N >= 2, and consider a class of some Weingarten hypersurfaces in RN+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 equations. The special case for some Monge-Ampere-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.
