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Analysis IV

Linear and Boundary Integral Equations

  • Book
  • © 1991

Overview

Editors:
  1. V. G. Maz’ya

    1. Department of Mathematics, University of Linköping, Linköping, Sweden

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    You can also search for this editor in PubMed   Google Scholar

  2. S. M. Nikol’skiĭ

    1. Steklov Mathematical Institute, Moscow, USSR

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 27)

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-vii
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  2. Linear Integral Equations

    • S. Prössdorf
    Pages 1-125

  3. Boundary Integral Equations

    • V. G. Maz’ya
    Pages 127-222

  4. Back Matter

    Pages 223-236
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Keywords

About this book

A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integralequations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind.

Editors and Affiliations

  • Department of Mathematics, University of Linköping, Linköping, Sweden

    V. G. Maz’ya

  • Steklov Mathematical Institute, Moscow, USSR

    S. M. Nikol’skiĭ

Bibliographic Information

  • Book Title: Analysis IV

  • Book Subtitle: Linear and Boundary Integral Equations

  • Editors: V. G. Maz’ya, S. M. Nikol’skiĭ

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-642-58175-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Hardcover ISBN: 978-3-540-51997-3Published: 05 April 1991

  • Softcover ISBN: 978-3-642-63491-8Published: 01 November 2012

  • eBook ISBN: 978-3-642-58175-5Published: 06 December 2012

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: VII, 236

  • Additional Information: Original Russian edition published by Publisher VINITI, Moscow, 1988

  • Topics: Potential Theory

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