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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The boundary Harnack inequality for infinity harmonic functions in the plane


Authors: John L. Lewis and Kaj Nyström
Journal: Proc. Amer. Math. Soc. 136 (2008), 1311-1323
MSC (2000): Primary 35J25, 35J70
Published electronically: December 6, 2007
MathSciNet review: 2367105
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Abstract: We prove the boundary Harnack inequality for positive infinity harmonic functions vanishing on a portion of the boundary of a bounded domain $ \Omega\subset\mathbf R^2$ under the assumption that $ \partial\Omega$ is a quasicircle.


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Additional Information

John L. Lewis
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email: john@ms.uky.edu

Kaj Nyström
Affiliation: Department of Mathematics, Umeå University, S-90187 Umeå, Sweden
Email: kaj.nystrom@math.umu.se

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09180-0
PII: S 0002-9939(07)09180-0
Keywords: Infinity Laplacian, infinity harmonic function, boundary Harnack inequality, quasicircle.
Received by editor(s): January 16, 2007
Published electronically: December 6, 2007
Additional Notes: The first author was partially supported by NSF grant DMS-055228.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society