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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.

References [Enhancements On Off] (What's this?)

  • [1] O. D. Kellogg, Potential functions on the boundary of their regions of definition, Trans. Amer. Math. Soc. 9 (1908), 39-50. MR 1500801
  • [2] E. J. Specht and H. T. Jones, Compactness of the Neumann-Poincaré operator, Trans. Amer. Math. Soc. 140 (1969), 353-366. MR 0402080 (53:5903)
  • [3] S. E. Warschawski, On the solution of the Lichtenstein-Gershgorin integral equation in conformal maps, Nat. Bur. Standards Appl. Math. Ser., no. 42, U.S. Government Printing Office, Washingon, D.C., 1955. MR 17, 540. MR 0074121 (17:540a)

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Keywords: Dirichlet problem, Neumann problem, integral equation, single-layer distribution, double-layer distribution
Article copyright: © Copyright 1973 American Mathematical Society

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