The smoothness of the solution to a two-dimensional integral equation with logarithmic kernel
type: Item
instance of: scholarly article
title: The smoothness of the solution to a two-dimensional integral equation with logarithmic kernel
zbMATH Open document ID: 0787.45002
DOI: 10.4171/ZAA/564
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1994-05-19T00:00:00Z
review text: The author studies properties of the solution of the integral equation \[ u(x)=\int_ \Omega a(x,y)\ln | x-y | u(y) dy+f(x),\;x \in \Omega \] where \(\Omega \subset \mathbb{R}^ 2\) is an open bounded set with a piecewise Lyapunov boundary \(\partial \Omega\) and \(f\) and \(a\) are sufficiently smooth functions. She describes the leading singular parts of the derivatives of an arbitrary order of the solution depending on the smoothness properties of \(\partial \Omega\).
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 429273
zbMATH Keywords: logarithmic kernel
zbMATH Keywords: weakly singular integral equations
zbMATH Keywords: smoothness of solution
zbMATH Keywords: leading singular parts
author: Urve Kangro
reviewed by: G. Vainikko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/564
OpenAlex ID: W1482205005
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description: scientific article; zbMATH DE number 429273