A liouville-type theorem for some weingarten hypersurfaces

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)887-895
ページ数9
ジャーナルDiscrete and Continuous Dynamical Systems - Series S
4
4
DOI
出版ステータスPublished - 2011 8
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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