Lower bounds for the half-plane capacity of compact sets and symmetrization
Journal Article
·
· Sbornik. Mathematics
- Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok (Russian Federation)
Given a bounded relatively closed subset E of the upper half-plane H={l_brace}z:Imz>0{r_brace}, a new representation of the half-plane capacity of E is obtained in terms of the inner radius of the connected component of the set H/E which goes off to infinity. For this capacity, new lower bounds in terms of the capacities of sets obtained by application of a series of geometric transformations of the set E, including the Steiner and circular symmetrizations, are established, and its behaviour under linear and radial averaging transformations of families of compact sets {l_brace}E{sub k{r_brace}k=1}{sup n} is examined. Bibliography: 10 titles.
- OSTI ID:
- 21592584
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 201; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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