On the behaviour of ∞-harmonic functions on some special unbounded domains

Tilak Bhattacharya

Vol. 219 (2005), No. 2, 237–253

DOI: 10.2140/pjm.2005.219.237

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 affine, 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 2000

Primary: 35J60, 35J70

Milestones

Received: 21 October 2003

Revised: 3 May 2004

Published: 1 April 2005