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Transactions of the American Mathematical Society

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An electromagnetic inverse problem in chiral media


Author: Stephen R. McDowall
Journal: Trans. Amer. Math. Soc. 352 (2000), 2993-3013
MSC (1991): Primary 35R30, 35Q60; Secondary 35S15
DOI: https://doi.org/10.1090/S0002-9947-00-02518-6
Published electronically: March 29, 2000
MathSciNet review: 1675214
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Abstract: We consider the inverse boundary value problem for Maxwell's equations that takes into account the chirality of a body in ${\mathbb R}^3$. More precisely, we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters, namely the conductivity, electric permittivity, magnetic permeability and chirality, in the interior. We rewrite Maxwell's equations as a first order perturbation of the Laplacian and construct exponentially growing solutions, and obtain the result in the spirit of complex geometrical optics.


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Additional Information

Stephen R. McDowall
Affiliation: Department of Mathematics, Universtiy of Washington, Box 354350, Seattle, Washington 98195-4350
Address at time of publication: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: mcdowall@math.rochester.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02518-6
Keywords: Inverse boundary value problems, Maxwell's equations, chirality, interior determination
Received by editor(s): June 9, 1997
Published electronically: March 29, 2000
Additional Notes: The author was partially supported by NSF Grant DMS-9705792
Article copyright: © Copyright 2000 American Mathematical Society

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