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Surface potential

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The potential of a measure that is concentrated on a certain surface. Two forms of a surface potential are used in handling major boundary value problems in potential theory: the simple-layer potential

produced by a measure distributed on a surface with density , ; and the double-layer potential

produced by a measure distributed on with density . Physically, a simple-layer potential is interpreted as the potential of electrical charges with density , and a double-layer potential is the potential of dipoles with density (see also Multi-pole potential).


Comments

References

[a1] O.D. Kellogg, "Foundations of potential theory" , Dover, reprint (1953) (Re-issue: Springer, 1967)
How to Cite This Entry:
Surface potential. E.D. Solomentsev (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Surface_potential&oldid=12154
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098