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

DOI:
https://doi.org/10.1090/S0002-9939-1973-0315144-6

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 , what distribution of charge on will produce a potential having specified values on ? The paper also indicates briefly how the integral equation is useful in simplifying certain proofs and extending certain theorems in potential theory.

**[1]**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**, https://doi.org/10.1090/S0002-9947-1908-1500801-0**[2]**E. J. Specht and H. T. Jones,*Compactness of the Neumann-Poincaré operator*, Trans. Amer. Math. Soc.**140**(1969), 353–366. MR**0402080**, https://doi.org/10.1090/S0002-9947-1969-0402080-3**[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**

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Additional Information

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