Inversion of some two-dimensional integral equations
type: Item
instance of: scholarly article
title: Inversion of some two-dimensional integral equations
zbMATH Open document ID: 0596.45001
DOI: 10.1007/BF01057437
author: M. V. Khaj
published in: Ukrainian Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: The author considers the integral equation \[ (1)\quad \iint_{S}(\gamma (\xi)/| x-\xi |^{1+\nu})d_{\xi}S=g(x),\quad x\in S,\quad 0\leq \nu \leq 2,\quad \nu \neq 1, \] where \(\gamma\) is unknown function, \(g\in L^ 2\), S is a plane domain. He obtains the solution of (1) by quadrature, when S is a halfplane or a disk. Classes of functions \(\gamma\) and g for which the solution is unique are indicated.
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 3960227
zbMATH Keywords: two-dimensional integral equation
zbMATH Keywords: unique solution
reviewed by: A. V. Bukhvalov
MaRDI profile type: Publication
cites work: Inverse problems of the plane theory of elasticity
cites work: Q4072052
full work available at URL: https://doi.org/10.1007/bf01057437
OpenAlex ID: W2065514370
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description: scientific article; zbMATH DE number 3960227