On a problem of nonoverlapping domains

V. A. Pchelintsev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number6
StatePublished - 1 Dec 2012
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics

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