An integral equation arising in potential theory
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- by H. T. Jones and E. J. Specht
- Proc. Amer. Math. Soc. 38 (1973), 349-354
- DOI: https://doi.org/10.1090/S0002-9939-1973-0315144-6
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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
- O. D. Kellogg, Potential functions on the boundary of their regions of definition, Trans. Amer. Math. Soc. 9 (1908), no. 1, 39–50. MR 1500801, DOI 10.1090/S0002-9947-1908-1500801-0
- E. J. Specht and H. T. Jones, Compactness of the Neumann-Poincaré operator, Trans. Amer. Math. Soc. 140 (1969), 353–366. MR 402080, DOI 10.1090/S0002-9947-1969-0402080-3
- S. E. Warschawski, On the solution of the Lichtenstein-Gershgorin integral equation in conformal mapping. I. Theory, Experiments in the computation of conformal maps, National Bureau of Standards Applied Mathematics Series, No. 42, U.S. Government Printing Office, Washington, D.C., 1955, pp. 7–29. MR 0074121
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 349-354
- MSC: Primary 31A25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0315144-6
- MathSciNet review: 0315144