Boundary Value Problems

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

Boundary Value Problems20072007:078029

https://doi.org/10.1155/2007/78029

©  Tilak Bhattacharya. 2007

Received: 27 June 2006

Accepted: 27 October 2006

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Western Kentucky University

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Copyright

© Tilak Bhattacharya. 2007

This article is published under license to BioMed Central Ltd. 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.