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Characterization of the Robin function by extremal problems.
- Source :
- Georgian Mathematical Journal; Sep2014, Vol. 21 Issue 3, p267-271, 5p
- Publication Year :
- 2014
-
Abstract
- In [`Robin function and conformal welding - A new proof of the existence', submitted] a new proof of the existence of the Robin function is given using conformal welding. This proof is essentially based on the simply connected case and a conformal mapping which maps the domain onto a complement of a disk and a system of radial spires. The aim of this note is to show that this proof also has a wider meaning, namely that this mapping is the unique solution of extremal problems, which minimizes the length or the diameter of a subset of the boundary curve. As a consequence we obtain sharp inequalities for the Robin capacity and the logarithmic capacity. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1072947X
- Volume :
- 21
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Georgian Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 98563854
- Full Text :
- https://doi.org/10.1515/gmj-2014-0027