Abstract
Harmonic functions in a domain may be represented as simple-layer or double-layer potentials, generated by hypothetical source density distributions on the boundary which satisfy Fredholm integral equations. An alternative formulation is via Green’s formula, in which the boundary data themselves function as source density distributions, so yielding Fredholm integral equations satisfied by the boundary data. The two approaches are theoretically equivalent, and we show how the second provides some insight into the first.
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List of References
Jaswon, M.A. & Symm, G.T. (1977). Integral Equation Methods in Potential Theory and Elastostatics. Academic Press: London & New York.
Kupradze, V.D. (1965). Potential Methods in the Theory of Elasticity. Israel Program for Scientific Translations: Jerusalem.
Rizzo, F.J. (1967). An integral equation approach to boundary value problems of classical elastostatics. Quart. App. Math. 25(1), 83–95.
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© 1981 Springer-Verlag Berlin Heidelberg
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Jaswon, M.A. (1981). Some Theoretical Aspects of Boundary Integral Equations. In: Brebbia, C.A. (eds) Boundary Element Methods. Boundary Elements, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11270-0_25
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DOI: https://doi.org/10.1007/978-3-662-11270-0_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11272-4
Online ISBN: 978-3-662-11270-0
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