Vol. 10, No. 3, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 6, 1605–1954
Issue 5, 1269–1603
Issue 4, 945–1268
Issue 3, 627–944
Issue 2, 317–625
Issue 1, 1–316

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
The one-phase problem for harmonic measure in two-sided NTA domains

Jonas Azzam, Mihalis Mourgoglou and Xavier Tolsa

Vol. 10 (2017), No. 3, 559–588
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.

Keywords
harmonic measure, nontangentially accessible (NTA) domains, VMO, Poisson kernel, free boundary problem
Mathematical Subject Classification 2010
Primary: 31B25, 31A15, 31B15, 35R35
Milestones
Received: 28 April 2016
Accepted: 13 February 2017
Published: 17 April 2017
Authors
Jonas Azzam
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Edifici C Facultat de Ciències
08193 Bellaterra
Catalonia
Mihalis Mourgoglou
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Edifici C Facultat de Ciències
08193 Bellaterra
Catalonia
Xavier Tolsa
Department of Mathematics
Universitat Autònoma de Barcelona
08193 Bellaterra
Catalonia
ICREA
Passeig Lluís Companys, 23
08010 Barcelona
Catalonia