Open Access Research Article

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

Tilak Bhattacharya

Author Affiliations

Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA

Boundary Value Problems 2007, 2007:078029  doi:10.1155/2007/78029

Published: 17 January 2007

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.