On the behaviour of ∞-harmonic functions on some special unbounded domains
Tilak Bhattacharya · Pacific Journal of Mathematics · 2005
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 affine, and in the second case u is radial and linear.We also discuss growth rates in an infinite strip.