Abstract

We study nonnegative ∞-harmonic functions defined on unbounded domains, in particular the half-space and the exterior of the unit closed ball. We prove that if such a function u vanishes continuously on the boundary then in the first case u is afine, and in the second case u is radial and linear. We also discuss growth rates in an infinite strip.

Keywords

∞-harmonic functions, viscosity solutions, growth rates, unbounded domains

Mathematical Subject Classification

Primary: 35J60, 35J70

Authors