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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., 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. doi:10.1090/S0894-0347-08-00601-2
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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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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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 | ||||
Official Date: | July 2009 | ||||
Dates: |
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Volume: | Vol.22 | ||||
Number: | No.3 | ||||
Number of Pages: | 26 | ||||
Page Range: | pp. 771-796 | ||||
DOI: | 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) |
Data sourced from Thomson Reuters' Web of Knowledge
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