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An estimate of harmonic measure in Ṟd, d ≧ 2

Published online by Cambridge University Press:  14 February 2012

Matts Essén
Matts Essén
Affiliation:
Department of Mathematics, Royal Institute of Technology, Stockholm
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Synopsis

Let D be an open connected subset of the open unit ball in Ṟd, d ≧ 2. We give an estimate of the harmonic measure of ∂D∩{|x| = 1} with respect to D. This estimate depends in a simple way on the geometry of D. An essential tool is a rearrangement theorem for differential inequalities. When d = 2, examples are given which illustrate the precision of the results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 129 - 138
Copyright
Copyright © Royal Society of Edinburgh 1977

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