Estimates of the products of inner radii for partially nonoverlapping domains of the complex plane
- Authors: Dvorak I.Y.1
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Affiliations:
- Institute of Mathematics of the National Academy of Sciences of Ukraine
- Issue: Vol 241, No 1 (2019)
- Pages: 36-46
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242853
- DOI: https://doi.org/10.1007/s10958-019-04405-8
- ID: 242853
Cite item
Abstract
Two problems of description of extremal configurations maximizing a product of the inner radii of mutually nonoverlapping domains are studied. One of the problems is analyzed in a more general situation: instead of nonoverlapping domains, the domains under the condition of partial disjointness are considered. The well-known problem posed in the work by V. N. Dubinin in 1988 is solved by Theorems 1 and 2. We study also the problem of maximum of a functional with the additional condition of symmetry defined by the domain G0. Theorems 3 and 4 give its partial solution.
About the authors
Inna Ya. Dvorak
Institute of Mathematics of the National Academy of Sciences of Ukraine
Author for correspondence.
Email: dvorakinna@gmail.com
Ukraine, Kyiv