THE WEAK-A∞ PROPERTY OF HARMONIC AND p-HARMONIC MEASURES IMPLIES UNIFORM RECTIFIABILITY

被引：38

作者：

Hofmann, Steve ^{[1
]}

Le, Phi ^{[2
]}

Maria Martell, Jose ^{[3
]}

Nystrom, Kaj ^{[4
]}

机构：

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

[2] Syracuse Univ, Math Dept, 215 Carnegie Bldg, Syracuse, NY 13244 USA

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

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

来源：

ANALYSIS & PDE | 2017年 / 10卷 / 03期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

harmonic measure and p-harmonic measure; Poisson kernel; uniform rectifiability; Carleson measures; Green function; weak-A(infinity); ELLIPTIC-OPERATORS; BOUNDARY-BEHAVIOR; POISSON KERNELS; RIESZ TRANSFORM; REIFENBERG FLAT; REGULARITY;

D O I：

10.2140/apde.2017.10.513

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let E subset of Rn+1, n >= 2, be an Ahlfors-David regular set of dimension n. We show that the weak- A 1 property of harmonic measure, for the open set Omega: =Rn+1 \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, p-harmonic measure, associated to the p-Laplace operator, 1 < p < infinity.

引用

页码：513 / 558

页数：46

共 41 条

[31] Poisson kernel characterization of Reifenberg flat chord arc domains
Kenig, CE
Toro, T
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2003, 36 (03): : 323 - 401
[32] Kilpeläinen T, 2003, ANN ACAD SCI FENN-M, V28, P181
[33] Uniqueness in a free boundary problem
Lewis, John L.
Vogel, Andrew L.
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (11) : 1591 - 1614
[34] REGULARITY AND FREE BOUNDARY REGULARITY FOR THE p-LAPLACE OPERATOR IN REIFENBERG FLAT AND AHLFORS REGULAR DOMAINS
Lewis, John L.
Nystrom, Kaj
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 25 (03) : 827 - 862
[35] Symmetry theorems and uniform rectifiability
Lewis, John L.
Vogel, Andrew L.
[J]. BOUNDARY VALUE PROBLEMS, 2007, 2007 (1)
[36] The Cauchy integral, analytic capacity, and uniform rectifiability
Mattila, P
Melnikov, MS
Verdera, J
[J]. ANNALS OF MATHEMATICS, 1996, 144 (01) : 127 - 136
[37] Mourgoglou M., 2015, PREPRINT
[38] THE RIESZ TRANSFORM, RECTIFIABILITY, AND REMOVABILITY FOR LIPSCHITZ HARMONIC FUNCTIONS
Nazarov, Fedor
Tolsa, Xavier
Volberg, Alexander
[J]. PUBLICACIONS MATEMATIQUES, 2014, 58 (02) : 517 - 532
[39] On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
Nazarov, Fedor
Tolsa, Xavier
Volberg, Alexander
[J]. ACTA MATHEMATICA, 2014, 213 (02) : 237 - 321
[40] LOCAL BEHAVIOR OF SOLUTIONS OF QUASI-LINEAR EQUATIONS
SERRIN, J
[J]. ACTA MATHEMATICA, 1964, 111 (3-4) : 247 - 302

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