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Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions

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Kenig, Carlos E., 1953-, Preiss, David and Toro, Tatiana. (2009) Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions. Journal of the American Mathematical Society, Vol.22 (No.3). pp. 771-796. ISSN 0894-0347

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Official URL: http://dx.doi.org/10.1090/S0894-0347-08-00601-2

Abstract

In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity for the harmonic measure $ \omega^+$ of a domain $ \Omega=\Omega^+\subset\mathbb{R}^n$ and the harmonic measure $ \omega^-$ of $ \Omega^-$, $ \Omega^-=$int$ (\Omega^c)$, in dimension $ n\ge 3$.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Measure theory, Spaces of measures, Potential theory (Mathematics), Mathematical analysis
Journal or Publication Title:	Journal of the American Mathematical Society
Publisher:	American Mathematical Society
ISSN:	0894-0347
Date:	July 2009
Volume:	Vol.22
Number:	No.3
Number of Pages:	26
Page Range:	pp. 771-796
Identification Number:	10.1090/S0894-0347-08-00601-2
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	National Science Foundation (U.S.) (NSF)
Grant number:	DMS-0456583 (NSF), DMS-0600915 (NSF)
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URI:	http://wrap.warwick.ac.uk/id/eprint/2263