An inverse problem for the double layer potential

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We consider an inverse problem for the double layer potential which can be formulated, somewhat loosely, as follows. For which smoothly bounded domains D in Euclidian space does the operator J, which maps a function on the boundary to the boundary values of its double layer potential, admit the eigenvalue 1/2. The question is motivated by Fredholm's solution to the Dirichlet problem by means of the double layer potential.

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Classical Analysis and ODEs, Complex Variables, 31A25, 31B20

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http://salesiana.dossiersoluciones.com/handle/123456789/62102

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108200
 http://arxiv.org/abs/math/0108200

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arXiv