On the approximation of singular integral equations by equations with smooth kernels
type: Item
instance of: scholarly article
title: On the approximation of singular integral equations by equations with smooth kernels
zbMATH Open document ID: 0827.45002
DOI: 10.1007/BF01203095
author: Siegfried Prössdorf
author: Roland Duduchava
published in: Integral Equations and Operator Theory
publication date: 1995-12-13T00:00:00Z
review text: Singular integral equations with Cauchy kernel and piecewise-continuous matrix coefficients on open and closed smooth curves \(\Gamma\) are replaced by integral equations with smooth kernels of the form \((t- \tau)[(t- \tau)^2- n^2(t) \varepsilon^2]^{- 1}\), \(\varepsilon\to 0\), where \(n(t)\), \(t\in \Gamma\), is a continuous field of unit vectors non-tangential to \(\Gamma\). Necessary and sufficient conditions are given, under which the approximating equations have unique solutions and these solutions converge to the solution of the original equation. For the scalar case and the space \(L_2(\Gamma)\) these conditions coincide with the strong ellipticity of the given equation.
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 45L05
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 764055
zbMATH Keywords: convergence
zbMATH Keywords: singular integral equations
zbMATH Keywords: Cauchy kernel
zbMATH Keywords: smooth kernels
zbMATH Keywords: strong ellipticity
reviewed by: Zongyi Hou
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01203095
OpenAlex ID: W1988239376
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description: scientific article; zbMATH DE number 764055