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The weak-A property of harmonic and p-harmonic measures implies uniform rectifiability
University of Missouri, Columbia, USA.
University of Missouri, Columbia, USA.
Instituto de Ciencias Matematicas, Madrid, Spain.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206XArticle in journal (Refereed) Accepted
Abstract [en]

Let $E\subset \ree$, $n\ge 2$, be an Ahlfors-David regular set of dimension $n$. We show that the weak-$A_\infty$ property of harmonic measure, for the open set$\Omega:= \ree\setminus E$, 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, $1<p<\infty$.

Place, publisher, year, edition, pages
2015.
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Mathematics
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URN: urn:nbn:se:uu:diva-267929OAI: oai:DiVA.org:uu-267929DiVA: diva2:874894
Available from: 2015-11-30 Created: 2015-11-30 Last updated: 2017-12-01Bibliographically approved

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arXiv:1511.09270

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Nyström, Kaj

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