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Harmonic balls and the two-phase Schwarz function
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2013 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 58, no 6, 837-852 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we introduce the concept of harmonic balls in sub-domains of (n), through a mean-value property for a subclass of harmonic functions on such domains. In the complex plane, and for analytic functions, a similar concept fails to exist due to the fact that analytic functions cannot have prescribed data on the boundary. Nevertheless, a two-phase version of the problem does exist, and gives rise to the generalization of the well-known Schwarz function to the case of a two-phase Schwarz function. Our primary goal is to derive simple properties for these problems, and tease the appetites of experts working on Schwarz function and related topics. Hopefully these two concepts will provoke further study of the topic.

Place, publisher, year, edition, pages
2013. Vol. 58, no 6, 837-852 p.
Keyword [en]
Schwarz function, mean-value property, harmonic functions, two-phase free boundary, quadrature domains, Primary: 35R35, 31A05, 31B05, 31B20
National Category
URN: urn:nbn:se:kth:diva-124282DOI: 10.1080/17476933.2011.622046ISI: 000319380200010ScopusID: 2-s2.0-84878636601OAI: diva2:634939

QC 20130702

Available from: 2013-07-02 Created: 2013-06-28 Last updated: 2013-07-02Bibliographically approved

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Shahgholian, Henrik
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