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

A Boundary Harnack Principle for Infinity-Laplacian and Some Related Results

Tilak Bhattacharya

 Department of Mathematics, Western Kentucky University, Bowling Green 42101, KY, USA
Received 27 June 2006; Revised 27 October 2006; Accepted 27 October 2006

Recommended by José Miguel Urbano

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.