On an extremal problem for nonoverlapping domains | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2018. № 52. DOI: 10.17223/19988621/52/2

On an extremal problem for nonoverlapping domains

The paper considers the problem of finding the range of the functional I = J(f (z₀), f (z₀), F (Z₀), F (Z ₀)) defined on the class M of functions pairs (f(z),F(Z)) that are univalent in the system of the disk and the interior of the disk, using the method of internal variations. We establish that the range of this functional is bounded by the curve whose equation is written in terms of elliptic integrals, depending on the parameters of the functional I.

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Keywords

Method of internal variations, Univalent function, Nonoverlapping domains, Functional range, Elliptic integrals, метод внутренних вариаций, однолистные функции, неналегающие области, множество значений функционала, эллиптические интегралы

Authors

Name	Organization	E-mail
Pchelintsev Evgeny A.	Tomsk State University	evgen-pch@yandex.ru
Pchelintsev Valerii A.	Tomsk Polytechnic University	vpchelintsev@vtomske.ru

Всего: 2

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