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An inverse problem for the double layer potential

P. Ebenfelt·D. Khavinson·H. S. Shapiro
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Abstract

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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P. Ebenfelt, D. Khavinson, H. S. Shapiro. 2001-08-29. An inverse problem for the double layer potential. https://arxiv.org/abs/math/0108200

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