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Boundary Value Problems
Boundary Value Problems Cover Image
  • Research Article
  • Open Access

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:

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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Related Result

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Authors’ Affiliations

(1)
Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA

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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.

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