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Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 7, Pages 39–47 (Mi ivm9481)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-41-160003_р_а


DOI: https://doi.org/10.26907/0021-3446-2019-7-39-47

Full text: PDF file (362 kB)
References: PDF file   HTML file

UDC: 517.544
Received: 27.05.2018
Revised: 07.08.2018
Accepted: 26.09.2018

Citation: B. A. Kats, “Zigzag-like and spiral-like arcs in boundary-value problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 7, 39–47

Citation in format AMSBIB
\Bibitem{Kat19}
\by B.~A.~Kats
\paper Zigzag-like and spiral-like arcs in boundary-value problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 7
\pages 39--47
\mathnet{http://mi.mathnet.ru/ivm9481}
\crossref{https://doi.org/10.26907/0021-3446-2019-7-39-47}


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