The weak-A∞ property of harmonic and p-harmonic measures implies uniform rectifiability
نویسندگان
چکیده
منابع مشابه
THE WEAK-A∞ PROPERTY OF HARMONIC AND p-HARMONIC MEASURES IMPLIES UNIFORM RECTIFIABILITY
Let E ⊂ Rn+1, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A∞ property of harmonic measure, for the open set Ω := 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 < ∞.
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ژورنال
عنوان ژورنال: Analysis & PDE
سال: 2017
ISSN: 1948-206X,2157-5045
DOI: 10.2140/apde.2017.10.513