## Abstract

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 language | English |
---|---|

Pages (from-to) | 887-895 |

Number of pages | 9 |

Journal | Discrete and Continuous Dynamical Systems - Series S |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Aug |

Externally published | Yes |

## Keywords

- Liouville-type theorem
- Viscosity solutions
- Weingarten hypersurfaces

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics