Abstract
The solution of boundary value problems for partial differential equations is one of the most important field of applications for integral equations. About a century ago the systematic development of the theory of integral equations was initiated by the treatment of boundary value problems and there has been an ongoing fruitful interaction between these two areas of applied mathematics. It is the aim of this chapter to introduce the main ideas of this field by studying the basic boundary value problems of potential theory. For the sake of simplicity we shall confine our presentation to the case of two and three space dimensions. The extension to more than three dimensions is straightforward. As we shall see, the treatment of the boundary integral equations for the potential theoretic boundary value problems delivers an instructive example for the application of the Fredholm alternative since its both cases occur in a natural way.
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© 1989 Springer-Verlag Berlin Heidelberg
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Kress, R. (1989). Potential Theory. In: Linear Integral Equations. Applied Mathematical Sciences, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97146-4_6
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DOI: https://doi.org/10.1007/978-3-642-97146-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-97148-8
Online ISBN: 978-3-642-97146-4
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