---

＜電子ブック＞
Analysis IV : Linear and Boundary Integral Equations / by V.G. Maz'ya ; edited by S. M. Nikol'skii
(Encyclopaedia of Mathematical Sciences ; 27)

版	1st ed. 1991.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	VII, 236 p : online resource
著者標目	*Maz'ya, V.G author Nikol'skii, S. M editor SpringerLink (Online service)
件　名	LCSH:Potential theory (Mathematics) FREE:Potential Theory
一般注記	I. Linear Integral Equations -- II. Boundary Integral Equations -- Author Index 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 HTTP:URL=https://doi.org/10.1007/978-3-642-58175-5

 類似資料