L. I. Vafina, I. G. Salekhova, “The Schwarz problem in the case of denumerable set of intervals”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 2,Pages <nobr>10

This article is cited in 2 papers

The Schwarz problem in the case of denumerable set of intervals

L. I. Vafina, I. G. Salekhova

Chair of Differential Equations, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We solve a Schwarz problem for a plane domain whose boundary is a union of denumerable set of segments (including those arranged periodically) with an accumulation point at infinity. The problem is solved by the reduction to the corresponding Riemann problem in the case of a denumerable set of contours, including those arranged periodically.

Keywords: Schwarz problem for a plane, Riemann problem, singly periodic arrangement of segments, singly periodic function, doubly periodic arrangement of segments, elliptic function, quasi-elliptic function.

UDC: 517.544

Received: 02.07.2014
Revised: 23.03.2015