Transformation of the Abel integral equation with nonsmooth data into an integral equation of the second kind
type: Item
instance of: scholarly article
title: Transformation of the Abel integral equation with nonsmooth data into an integral equation of the second kind
zbMATH Open document ID: 0944.45003
author: V. L. Gryn'
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-06-18T00:00:00Z
review text: A method of transformation of the linear Abel integral equation with nonsmooth input data into an integral equation of the second kind in the spaces \(L_{p,h}\), \(C^{0+\mu}\) and \(C_{h_2}\) is proposed. The existence, uniqueness, nonexistence and nonuniqueness of its solutions are investigated, and estimates concerning the stability of solutions are obtained. The case when the kernel \(K(\nu,u)\in L_\rho(D_\varepsilon)\) satisfies \[ (\nu-u)^\beta\partial K(\nu,u)/\partial\nu\in L_r (0,\varepsilon, L_\xi(u,\varepsilon)) \] is analyzed.
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45M10
zbMATH DE Number: 1440445
zbMATH Keywords: integral equation of the second kind
zbMATH Keywords: linear Abel integral equation
zbMATH Keywords: stability
zbMATH Keywords: method of transformation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1440445