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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. 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

Official Date:

July 2009

Dates:

Date	Event
July 2009	Published

Volume:

Vol.22

Number:

No.3

Number of Pages:

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

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