Boundary Value Problems
Volume 2007 (2007), Article ID 78029, 17 pages
doi:10.1155/2007/78029

A boundary Harnack principle for infinity-Laplacian and some related results

Abstract

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.