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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. 771796. ISSN 08940347

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Official URL: http://dx.doi.org/10.1090/S0894034708006012
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:  08940347 
Official Date:  July 2009 
Volume:  Vol.22 
Number:  No.3 
Number of Pages:  26 
Page Range:  pp. 771796 
Identification Number:  10.1090/S0894034708006012 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
Funder:  National Science Foundation (U.S.) (NSF) 
Grant number:  DMS0456583 (NSF), DMS0600915 (NSF) 
References:  1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 
URI:  http://wrap.warwick.ac.uk/id/eprint/2263 
Data sourced from Thomson Reuters' Web of Knowledge
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