On a problem of nonoverlapping domains

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2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1119-1127
Number of pages9
JournalSiberian Mathematical Journal
Volume53
Issue number6
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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