The extremal problem for the area of an image of a disc

TitleThe extremal problem for the area of an image of a disc
Publication TypeJournal Article
Year of Publication2016
AuthorsSalimov, RR, Klishchuk, BA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.10.022
Issue10
SectionMathematics
Pagination22-27
Date Published10/2016
LanguageRussian
Abstract

We study the ring Q-homeomorphisms with respect to p-modulus, p ˃ 2, in the complex plane and establish lower bounds for the area of an image of a disc. The extremal problem concerning a minimization of the area functional is solved.
Keywordsarea functional, capacitor, p-capacitance of a capacitor, p-modulus of a family of curves, ring Q-homeomorphisms
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