On an extremal problem for nonoverlapping domains

E. A. Pchelintsev, V. A. Pchelintsev

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)13-24
Number of pages12
JournalVestnik Tomskogo Gosudarstvennogo Universiteta, Matematika i Mekhanika
Issue number52
DOIs
Publication statusPublished - 1 Jan 2018

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Keywords

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

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering
  • Mechanics of Materials
  • Mathematics(all)

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