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Harmonic balls and ...
Harmonic balls and the two-phase Schwarz function
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- Shahgholian, Henrik (författare)
- KTH,Matematik (Avd.),Royal Institute of Technology, Sweden
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- Sjödin, Tomas (författare)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan
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KTH Matematik (Avd) (creator_code:org_t)
- Taylor and Francis: STM, Behavioural Science and Public Health Titles / Taylor and Francis, 2013
- 2013
- Engelska.
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Ingår i: Complex Variables and Elliptic Equations. - : Taylor and Francis: STM, Behavioural Science and Public Health Titles / Taylor and Francis. - 1747-6933 .- 1747-6941. ; 58:6, s. 837-852
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Schwarz function
- mean-value property
- harmonic functions
- two-phase free boundary
- quadrature domains
- Primary: 35R35
- 31A05
- 31B05
- 31B20
- MATHEMATICS
- MATEMATIK
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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