THE ONE-PHASE PROBLEM FOR HARMONIC MEASURE IN TWO-SIDED NTA DOMAINS

被引：3
|
作者：
Azzam, Jonas [1 ]
Mourgoglou, Mihalis [1 ]
Tolsa, Xavier [2 ,3 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, Fac Ciencies, Edifici C, Bellaterra 08193, Catalonia, Spain
[2] Univ Autonoma Barcelona, Dept Math, Bellaterra 08193, Catalonia, Spain
[3] ICREA, Passeig Lluis Co 23, Barcelona 08010, Spain
来源：
ANALYSIS & PDE | 2017年 / 10卷 / 03期
基金：
欧洲研究理事会;
关键词：
harmonic measure; nontangentially accessible (NTA) domains; VMO; Poisson kernel; free boundary problem; FREE-BOUNDARY REGULARITY; HYPERSURFACES;
D O I：
10.2140/apde.2017.10.559
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that if Omega subset of R-3 is a two-sided NTA domain with AD-regular boundary such that the logarithm of the Poisson kernel belongs to VMO(sigma), where sigma is the surface measure of Omega, then the outer unit normal to partial derivative Omega belongs to VMO(sigma) 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.
引用
收藏
页码：559 / 588
页数：30
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