A liouville-type theorem for some weingarten hypersurfaces

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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.

Original languageEnglish
Pages (from-to)887-895
Number of pages9
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue number4
Publication statusPublished - 2011 Aug
Externally publishedYes


  • Liouville-type theorem
  • Viscosity solutions
  • Weingarten hypersurfaces

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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