Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Published electronically: March 29, 2000
MathSciNet review: 1675214
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. Lee J. and Uhlmann G., 1989, Determining Anisotropic Real-Analytic Conductivities by Boundary Measurements Comm. Pure Appl. Math. 42 1097-1112 MR 91a:35166
  • 2. Lakhtakia A., Varadan V. K. and Varadan V. V., 1989, Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics, Vol 335 (Berlin: Springer-Verlag) MR 90e:78001
  • 3. Leis L., 1986, Initial Bounday Value Problems in Mathematical Physics (New York: John Wiley and Sons Inc.) MR 87h:35083
  • 4. McDowall S., 1997, Boundary determination of material parameters from electromagnetic boundary information Inverse Problems 13 153-163 MR 98c:78010
  • 5. Nakamura G. and Uhlmann G., 1994, Global uniqueness for an inverse boundary problem arising in elasticity Invent. math. 118 457-474 MR 95i:35313
  • 6. Nirenberg L. and Walker H.F., 1973, The Null Spaces of Elliptic Partial Differnetial Operators in ${\mathbb R}^n$ J. Math. Anal. Appl 42 271-301 MR 47:9354
  • 7. Ola P., Päivärinta L. and Somersalo E., 1993, An Inverse Boundary Problem in Electrodynamics Duke Math. J. 70 617-653 MR 94i:35196
  • 8. Ola P. and Somersalo E., 1996, Electromagnetic Inverse Problems and Generalized Sommerfeld Potentials SIAM J. Appl. Math. 56 1129-1145 MR 97b:35194
  • 9. Reed M. and Simon B., 1972, Methods of Modern Mathematical Physics, Vol. I (New York: Academic Press) MR 58:12429a
  • 10. Shubin M. A., 1987, Pseudodifferential Operators and Spectral Theory (Berlin Heidelberg New York: Springer Series in Soviet Mathematics) MR 88c:47105
  • 11. Somersalo E., Isaacson D. and Cheney M., 1992, A Linearized Inverse Boundary Value Problem for Maxwell's Equations J. Comput. Appl. Math. 42 123-136 MR 93f:35242
  • 12. Sylvester J. and Uhlmann G., 1987, A global uniqueness theorem for an inverse boundary problem Annals of Math. 125 153-169 MR 88b:35205
  • 13. Tolmasky C., 1998, Exponentially growing solutions for non-smooth first-order perturbations of the Laplacian SIAM J. Math. Anal. 29 116-133
  • 14. Wendland W. L., 1979, Elliptic Systems in the Plane (London: Pitman) MR 80h:35053

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 35R30, 35Q60, 35S15

Retrieve articles in all journals with MSC (1991): 35R30, 35Q60, 35S15

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

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

American Mathematical Society