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An Inverse Problem for the Double Layer Potential

An Inverse Problem for the Double Layer Potential We consider the problem of determining for which domains Ω ⊂ R n the number 1/2 is an eigenvalue for the operator taking a function on the boundary ∂Ω to the boundary values of its double layer potential. This question arises naturally in I. Fredholm’s solution to the Dirichlet problem for the Laplace operator in Ω. In two dimensions, the problem is equivalent to a matching problem for analytic functions which seems to be of independent interest. We show that the existence of a nontrivial solution for the matching problem characterizes the disk in a certain class of domains in the complex plane. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

An Inverse Problem for the Double Layer Potential

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Publisher
Springer Journals
Copyright
Copyright © 2001 by Heldermann Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03320998
Publisher site
See Article on Publisher Site

Abstract

We consider the problem of determining for which domains Ω ⊂ R n the number 1/2 is an eigenvalue for the operator taking a function on the boundary ∂Ω to the boundary values of its double layer potential. This question arises naturally in I. Fredholm’s solution to the Dirichlet problem for the Laplace operator in Ω. In two dimensions, the problem is equivalent to a matching problem for analytic functions which seems to be of independent interest. We show that the existence of a nontrivial solution for the matching problem characterizes the disk in a certain class of domains in the complex plane.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References