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An existence theorem for Robin's equation

Published online by Cambridge University Press:  24 October 2008

R. Cade
R. Cade
Affiliation:
Department of Mathematics, University of Puerto Rico, Mayagüez, Puerto Rico
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Abstract

An existence theorem is proved for Robin's integral equation for the density of electric charge on a closed surface, under the assumptions that the surface is convex, smooth and twice continuously differentiable. The technique is essentially Neumann's method of the arithmetic mean, used by Robin himself to show that the solution, assumed to exist, can be successively approximated by a sequence. In order to facilitate the main argument of the proof, it is assumed initially that the Gaussian curvature is everywhere positive, but this restriction is subsequently removed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 489 - 498
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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