Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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, E-ISSN 1747-6941, 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
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-124282DOI: 10.1080/17476933.2011.622046ISI: 000319380200010Scopus ID: 2-s2.0-84878636601OAI: oai:DiVA.org:kth-124282DiVA: diva2:634939
Note

QC 20130702

Available from: 2013-07-02 Created: 2013-06-28 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Shahgholian, Henrik

Search in DiVA

By author/editor
Shahgholian, Henrik
By organisation
Mathematics (Div.)
In the same journal
Complex Variables and Elliptic Equations
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 83 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf