A new characterization of chord-arc domains

被引：49

作者：

Azzam, Jonas ^{[1
]}

Hofmann, Steve ^{[2
]}

Maria Martell, Jose ^{[3
]}

Nystrom, Kaj ^{[4
]}

Toro, Tatiana ^{[5
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Edifici C Fac Ciencies, E-08193 Bellaterra, Barcelona, Spain

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] CSIC, CSIC UAM UCM UC3M, Inst Ciencias Matemat, C Nicolas Cabrera 13-15, E-28049 Madrid, Spain

[4] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

[5] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2017年 / 19卷 / 04期

基金：

欧洲研究理事会; 瑞典研究理事会; 美国国家科学基金会;

关键词：

Chord-arc domains; NTA domains; 1-sided NTA domains; uniform domains; uniform rectifiability; Carleson measures; harmonic measure; A(infinity) Muckenhoupt weights; UNIFORM RECTIFIABILITY; HARMONIC MEASURE; EXTENSION-THEOREMS; POISSON KERNELS; REIFENBERG-FLAT; HYPERSURFACES; APPROXIMATION; OPERATOR;

D O I：

10.4171/JEMS/685

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 Rn+1, n >= 1, is a uniform domain (also known as a 1-sided NTA domain), i.e., a domain which enjoys interior corkscrew and Harnack chain conditions, then uniform rectifiability of the boundary of Omega implies the existence of exterior corkscrew points at all scales, so that in fact, Omega is a chord-arc domain, i.e., a domain with an Ahlfors-David regular boundary which satisfies both interior and exterior corkscrew conditions, and an interior Harnack chain condition. We discuss some implications of this result for theorems of F. and M. Riesz type, and for certain free boundary problems.

引用

页码：967 / 981

页数：15

共 24 条

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