Encyclopaedia of Mathematical Sciences

Analysis IV

Linear and Boundary Integral Equations

Editors: Maz'ya, V.G., Nikol'skii, S.M. (Eds.)

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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 integral equations 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.

Table of contents (1 chapter)

  • Boundary Integral Equations

    V. G. Maz’ya

    Pages 127-222

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eBook $69.99 net
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  • ISBN 978-3-642-58175-5
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $99.00 net
( price for USA )
  • ISBN 978-3-642-63491-8
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Analysis IV
Book Subtitle
Linear and Boundary Integral Equations
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
27
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58175-5
DOI
10.1007/978-3-642-58175-5
Softcover ISBN
978-3-642-63491-8
Series ISSN
0938-0396
Edition Number
1
Topics