This article is cited in 2 papers

On a problem of nonoverlapping domains

V. A. Pchelintsev

Tomsk State University, Mechanics and Mathematics Department, Tomsk, Russia

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.

UDC: 517.54

Received: 03.02.2012

 English version: Siberian Mathematical Journal, 2012, 53:6, 1119–1127

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