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

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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Correspondence to Tilak Bhattacharya.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bhattacharya, T. A Boundary Harnack Principle for Infinity-Laplacian and Some Related Results. Bound Value Probl 2007, 078029 (2007). https://doi.org/10.1155/2007/78029

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Keywords

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