On an extremal problem for nonoverlapping domains

E. A. Pchelintsev; V. A. Pchelintsev

doi:10.17223/19988621/52/2

On an extremal problem for nonoverlapping domains

E. A. Pchelintsev, V. A. Pchelintsev

Research output: Contribution to journal › Article › peer-review

Abstract

The paper considers the problem of finding the range of the functional I = J (f (z₀ ), f (z₀ ), F (ζ₀ ), F (ζ₀ )) defined on the class M of functions pairs (f (z ), F (ζ)) 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.

Original language	English
Pages (from-to)	13-24
Number of pages	12
Journal	Vestnik Tomskogo Gosudarstvennogo Universiteta, Matematika i Mekhanika
Issue number	52
DOIs	https://doi.org/10.17223/19988621/52/2
State	Published - 1 Jan 2018
Externally published	Yes

Keywords

Elliptic integrals
Functional range
Method of internal variations
Nonoverlapping domains
Univalent function

ASJC Scopus subject areas

Computational Mechanics
General Mathematics
Mechanics of Materials
Mechanical Engineering

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N2 - The paper considers the problem of finding the range of the functional I = J (f (z0 ), f (z0 ), F (ζ0 ), F (ζ0 )) defined on the class M of functions pairs (f (z ), F (ζ)) 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.

AB - The paper considers the problem of finding the range of the functional I = J (f (z0 ), f (z0 ), F (ζ0 ), F (ζ0 )) defined on the class M of functions pairs (f (z ), F (ζ)) 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.

KW - Elliptic integrals

KW - Functional range

KW - Method of internal variations

KW - Nonoverlapping domains

KW - Univalent function

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IS - 52

ER -

On an extremal problem for nonoverlapping domains

Abstract

Keywords

ASJC Scopus subject areas

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