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2017 The one-phase problem for harmonic measure in two-sided NTA domains
Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa
Anal. PDE 10(3): 559-588 (2017). DOI: 10.2140/apde.2017.10.559

Abstract

We show that if Ω 3 is a two-sided NTA domain with AD-regular boundary such that the logarithm of the Poisson kernel belongs to VMO(σ), where σ is the surface measure of Ω, then the outer unit normal to Ω belongs to VMO(σ) too. The analogous result fails for dimensions larger than 3. This answers a question posed by Kenig and Toro and also by Bortz and Hofmann.

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Jonas Azzam. Mihalis Mourgoglou. Xavier Tolsa. "The one-phase problem for harmonic measure in two-sided NTA domains." Anal. PDE 10 (3) 559 - 588, 2017. https://doi.org/10.2140/apde.2017.10.559

Information

Received: 28 April 2016; Accepted: 13 February 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1376.31007
MathSciNet: MR3641880
Digital Object Identifier: 10.2140/apde.2017.10.559

Subjects:
Primary: 31A15, 31B15, 31B25, 35R35

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2017
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