The skew derivative problem in the exterior of open curves in a plane
type: Item
instance of: scholarly article
title: The skew derivative problem in the exterior of open curves in a plane
zbMATH Open document ID: 0888.35027
DOI: 10.4171/ZAA/788
author: P. A. Krutitskii
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1998-06-04T00:00:00Z
review text: In several preceding papers, the author considered the Dirichlet and Neumann problems for the Helmholtz equation outside cuts in the plane [cf. Comput. Math. Math. Phys. 34, 1073--1090 and 1421--1431 (1994; Zbl 0835.35033 and Zbl 0835.35034)]. Utilizing related ideas, in the present paper the skew derivative problem for the two-dimensional Laplace equation is investigated in the exterior of open curves. The essential step is the reduction of the problem to a Fredholm integral equation of the second kind. Results on the existence, uniqueness, regularity and construction of solutions are obtained.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 31A25
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 1068009
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: regularity
reviewed by: M. Kracht
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/788
OpenAlex ID: W2085180847
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description: scientific article; zbMATH DE number 1068009