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The one-phase problem
for harmonic measure in two-sided NTA domains
Jonas Azzam, Mihalis Mourgoglou and Xavier Tolsa |
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Vol. 10 (2017), No. 3, 559–588
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Abstract |
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We show that if is a two-sided NTA domain with AD-regular boundary such that the logarithm of the Poisson kernel belongs to , where is the surface measure of , then the outer unit normal to belongs to too. The analogous result fails for dimensions larger than . 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
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Mathematical Subject Classification 2010
Primary: 31B25, 31A15, 31B15, 35R35
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Milestones
Received: 28 April 2016
Accepted: 13 February 2017
Published: 17 April 2017
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Authors |
| Jonas Azzam | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona Edifici C Facultat de Ciències 08193 Bellaterra Catalonia |
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| Mihalis Mourgoglou | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona Edifici C Facultat de Ciències 08193 Bellaterra Catalonia |
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| Xavier Tolsa | |
| Department of Mathematics Universitat Autònoma de Barcelona 08193 Bellaterra Catalonia |
ICREA Passeig Lluís Companys, 23 08010 Barcelona Catalonia |
| © 2017 MSP (Mathematical Sciences Publishers). |
