On the problem of V. N. Dubinin for symmetric multiply connected domains
- Authors: Vyhivska L.V.1
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Affiliations:
- Institute of Mathematics of the NAS of Ukraine
- Issue: Vol 229, No 1 (2018)
- Pages: 108-113
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240382
- DOI: https://doi.org/10.1007/s10958-018-3665-8
- ID: 240382
Cite item
Abstract
Abstract
The problem of maximum of the functional
is considered. Here, \( \upgamma \in \left(0,n\right],{a}_0=0,\kern0.5em \left|{a}_k\right|=1,k=\overline{1,n},{a}_k\in {B}_k\subset \overline{\mathrm{\mathbb{C}}},\kern0.5em k=\overline{0,n},\kern0.5em {\left\{{B}_k\right\}}_{k=1}^n \) are pairwise non-overlapping domains, \( {\left\{{B}_k\right\}}_{k=0}^n \) are symmetric domains with respect to the unit circle, and r(B; a) is the inner radius of the domain \( B\subset \overline{\mathrm{\mathbb{C}}} \) with respect to the point a ∈ B. For γ = 1 and n ≥ 2, the problem was formulated as an open problem by V. N. Dubinin in 1994. L. V. Kovalev solved the Dubinin problem in 2000. The article deals with finding the maximum of the functional In(γ) for γ > 1.
About the authors
Liudmyla V. Vyhivska
Institute of Mathematics of the NAS of Ukraine
Author for correspondence.
Email: liudmylavygivska@ukr.net
Ukraine, Kyiv