Analysis IV: Linear and Boundary Integral Equations (Encyclopaedia of Mathematical Sciences)

Maz'ya, V.G.

ISBN 10: 3642634915 / ISBN 13: 9783642634918

Editore: Springer, 2012

Riguardo questo articolo

Codice articolo ABLIING23Mar3113020232056

Dati bibliografici

• Titolo: Analysis IV: Linear and Boundary Integral Equations (Encyclopaedia of Mathematical Sciences)
• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3642634915
• ISBN 13: 9783642634918
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

I. Linear Integral Equations.- II. Boundary Integral Equations.- Author Index.