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This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Open Badges 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

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/078029

Received:27 June 2006
Revisions received:27 October 2006
Accepted:27 October 2006
Published:17 January 2007

© 2007 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.


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