This article is cited in 5 papers

Zigzag-like and spiral-like arcs in boundary-value problems

B. A. Kats

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: It the paper is dealing with curvilinear integrals over non-smooth paths with application in boundary-value problems. We show that geometry of end-points of the path is of importance for solvability of homogeneous Riemann boundary-value problem on this arc. On a zigzag-like path the numbers of solutions and conditions of solvability are the same as for smooth arcs, but for spiral-like paths these numbers can vary.

Keywords: non-smooth path, curvilinear integral, Cauchy type integral, Riemann boundary-value problem.

UDC: 517.544

Received: 27.05.2018
Revised: 07.08.2018
Accepted: 26.09.2018

DOI: 10.26907/0021-3446-2019-7-39-47

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:7, 33–40

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