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Siberian Mathematical Journal

, Volume 53, Issue 6, pp 1119–1127 | Cite as

On a problem of nonoverlapping domains

  • V. A. PchelintsevEmail author
Article

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].

Keywords

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

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia

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