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2017 The weak-$A_\infty$ property of harmonic and $p$-harmonic measures implies uniform rectifiability
Steve Hofmann, Long Le, José María Martell, Kaj Nyström
Anal. PDE 10(3): 513-558 (2017). DOI: 10.2140/apde.2017.10.513

Abstract

Let E n+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 := n+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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Steve Hofmann. Long Le. José María Martell. Kaj Nyström. "The weak-$A_\infty$ property of harmonic and $p$-harmonic measures implies uniform rectifiability." Anal. PDE 10 (3) 513 - 558, 2017. https://doi.org/10.2140/apde.2017.10.513

Information

Received: 12 February 2016; Accepted: 12 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1369.31006
MathSciNet: MR3641879
Digital Object Identifier: 10.2140/apde.2017.10.513

Subjects:
Primary: 31B05, 31B25, 35J08, 42B25, 42B37
Secondary: 28A75, 28A78

Rights: Copyright © 2017 Mathematical Sciences Publishers

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