On a problem of nonoverlapping domains

V. A. Pchelintsev

doi:10.1134/S003744661206016X

On a problem of nonoverlapping domains

V. A. Pchelintsev

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

2 Scopus citations

Abstract

We solve the problem of finding the range E of some functional on the class of pairs of functions univalent in the system of the disk and the interior of the disk for the arbitrary parameters characterizing the functional. We prove that E is connected and bounded. Using the method of internal variations and the parametric method, we find the equation of the boundary of E. The obtained results extend Lebedev's study [1].

Original language	English
Pages (from-to)	1119-1127
Number of pages	9
Journal	Siberian Mathematical Journal
Volume	53
Issue number	6
DOIs	https://doi.org/10.1134/S003744661206016X
State	Published - 1 Dec 2012
Externally published	Yes

Keywords

elliptic integrals
functional
method of internal variations
nonoverlapping domains
parametric method
range

ASJC Scopus subject areas

General Mathematics

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10.1134/S003744661206016X

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AB - We solve the problem of finding the range E of some functional on the class of pairs of functions univalent in the system of the disk and the interior of the disk for the arbitrary parameters characterizing the functional. We prove that E is connected and bounded. Using the method of internal variations and the parametric method, we find the equation of the boundary of E. The obtained results extend Lebedev's study [1].

KW - elliptic integrals

KW - functional

KW - method of internal variations

KW - nonoverlapping domains

KW - parametric method

KW - range

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JF - Siberian Mathematical Journal

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On a problem of nonoverlapping domains

Abstract

Keywords

ASJC Scopus subject areas

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