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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An integral equation arising in potential theory


Authors: H. T. Jones and E. J. Specht
Journal: Proc. Amer. Math. Soc. 38 (1973), 349-354
MSC: Primary 31A25
MathSciNet review: 0315144
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Abstract: This paper gives an integral equation, the solution of which is a solution of a classical problem in potential theory: Given a region with boundary $ \mathcal{B}$, what distribution of charge on $ \mathcal{B}$ will produce a potential having specified values on $ \mathcal{B}$? The paper also indicates briefly how the integral equation is useful in simplifying certain proofs and extending certain theorems in potential theory.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0315144-6
Keywords: Dirichlet problem, Neumann problem, integral equation, single-layer distribution, double-layer distribution
Article copyright: © Copyright 1973 American Mathematical Society