An inverse problem for the double layer potential
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
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.
Cite
@article{arxiv.math/0108200,
title = {An inverse problem for the double layer potential},
author = {P. Ebenfelt and D. Khavinson and H. S. Shapiro},
journal= {arXiv preprint arXiv:math/0108200},
year = {2007}
}