Jump boundary-value problem on a contour with elongate singularities
type: Item
instance of: scholarly article
title: Jump boundary-value problem on a contour with elongate singularities
zbMATH Open document ID: 1391.30053
DOI: 10.3103/S1066369X17010029
author: Boris A. Kats
author: S. R. Mironova
author: A. Yu. Pogodina
published in: Russian Mathematics
publication date: 2018-02-14T00:00:00Z
review text: The problem under consideration is the following: to find two analytic functions knowing their difference on a given contour. This problem is well known and has numerous applications. In the case of sufficiently smooth contours, it is investigated in the classical books devoted to the theory of linear conjugation for analytic functions and the theory of singular integral equations. In the case of contours from wider classes, the investigation needs essential additional efforts. The paper under review continues the work of the authors [Russ. Math. 59, No. 2, 57--61 (2015); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2015, No. 2, 70--75 (2015; Zbl 1327.30043)]. Let \(\Gamma\) be the image of an injective mapping \(\varphi: (0,1)\to \mathbb C\). If the set \(\overline{\Gamma}\setminus\Gamma\) has more than two points, then \(\Gamma\) is called a contour with elongate singularities. For such contours, under some additional assumptions and for some class of functions, solvability and uniqueness of the problem is proved
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 30E25
zbMATH DE Number: 6838071
zbMATH Keywords: jump problem for analytic functions
zbMATH Keywords: contour with singularities
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6838071