The boundary Harnack inequality for infinity harmonic functions in the plane

Lewis, John; Nyström, Kaj

doi:10.1090/S0002-9939-07-09180-0

The boundary Harnack inequality for infinity harmonic functions in the plane
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by John L. Lewis and Kaj Nyström

Proc. Amer. Math. Soc. 136 (2008), 1311-1323

DOI: https://doi.org/10.1090/S0002-9939-07-09180-0

Published electronically: December 6, 2007

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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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