The Asymptotic Behaviour of the Capacity as some Plates of the Condenser Degenerate into Points

Vladimir N. Dubinin
Additional contact information
Vladimir N. Dubinin: Far Eastern Federal University, Institute of Applied Mathematics

Chapter Chapter 2 in Condenser Capacities and Symmetrization in Geometric Function Theory, 2014, pp 25-60 from Springer

Abstract: Abstract In this section we have collected some definitions and properties of the functions mentioned in the title. For a domain B on the Riemann sphere $$\overline{\mathbb{C}}$$ and a point $$Z_0\;\in\;B,\; Z_0\;\neq\;\infty$$ assume that there exists a function $$gB(z,\;z_0)$$ which is continuous in $$\overline{\mathbb{C}}$$ , harmonic in B apart from z0, vanishes outside B, and has the following property: the function $$gB(z,\;z_0)\;+\;\mathrm{log}|z-z_{0}|$$ is harmonic in a neighbourhood of z0.

Keywords: Green Function; Connected Domain; Riemann Sphere; Analytic Curf; Nonempty Closed Subset (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0843-9_2

Ordering information: This item can be ordered from
http://www.springer.com/9783034808439

DOI: 10.1007/978-3-0348-0843-9_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().