An inverse problem for the double layer potential

2001/08/29 by P. Ebenfelt, Ebenfelt, P., D. Khavinson +3 · 1 citation
Mathematics · #31A25 #31B20 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:31A25 #msc:31B20

paper · pdf · doi:10.48550/arxiv.math/0108200

arxiv created 2001/08/29 · arxiv updated 2009/11/30

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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