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 |
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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