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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 6, Pages 1391–1400 (Mi smj2391)  
This article is cited in 2 scientific papers (total in 2 papers)

On a problem of nonoverlapping domains

V. A. Pchelintsev

Tomsk State University, Mechanics and Mathematics Department, Tomsk, Russia
Full-text PDF (302 kB) Citations (2)
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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.
Received: 03.02.2012
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 6, Pages 1119–1127
DOI: https://doi.org/10.1134/S003744661206016X
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. A. Pchelintsev, “On a problem of nonoverlapping domains”, Sibirsk. Mat. Zh., 53:6 (2012), 1391–1400; Siberian Math. J., 53:6 (2012), 1119–1127
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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