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

1Salimov, RR
1Klishchuk, BA
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 10:22-27
Section: Mathematics
Language: Russian

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.

Keywords: area functional, capacitor, p-capacitance of a capacitor, p-modulus of a family of curves, ring Q-homeomorphisms
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