Boundary Value Problems
Volume 2007 (2007), Article ID 78029, 17 pages
A Boundary Harnack Principle for Infinity-Laplacian and Some
Department of Mathematics, Western Kentucky University, Bowling Green 42101, KY, USA
Received 27 June 2006; Revised 27 October 2006; Accepted 27 October 2006
Academic Editor: José Miguel Urbano
Copyright © 2007 Tilak Bhattacharya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove a boundary comparison principle for positive
infinity-harmonic functions for smooth boundaries. As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic
functions in smooth bounded domains and the half-space,
and (b) the optimality of blowup rates of Aronsson's examples of singular solutions in cones.