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A new characterization of chord-arc domains
University of Washington, Seattle, 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.
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2015 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863Article in journal (Refereed) Accepted
Abstract [en]

We show that if $\om \subset \ree$, $n\geq 1$, is a uniform domain (aka 1-sided NTA domain), i.e., a domain which enjoys interior Corkscrew and Harnack Chain conditions, then uniform rectifiability of the boundary of $\om$ implies the existence of exterior Corkscrew points at all scales, so that in fact, $\om$ 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.

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Mathematical Analysis
URN: urn:nbn:se:uu:diva-226720OAI: oai:DiVA.org:uu-226720DiVA: diva2:727074
Available from: 2014-06-19 Created: 2014-06-19 Last updated: 2016-02-17

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