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Attainability by simply connected domains of optimal bounds for the polarization tensor

Published online by Cambridge University Press:  26 April 2006

HABIB AMMARI ,
YVES CAPDEBOSCQ ,
HYEONBAE KANG ,
EUNJOO KIM  and
MIKYOUNG LIM
HABIB AMMARI
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France email: ammari@cmapx.polytechnique.fr, eunjoo@cmapx.polytechnique.fr, mklim@cmapx.polytechnique.fr
YVES CAPDEBOSCQ
Affiliation:
Laboratoire de Mathématiques, Université de Versailles Saint-Quentin-en-Yvelines, 78035 Versailles Cedex, France email: Yves.Capdeboscq@math.uvsq.fr
HYEONBAE KANG
Affiliation:
Department of Mathematical Sciences and RIM, Seoul National University, Seoul 151-747, Korea email: hkang@math.snu.ac.kr
EUNJOO KIM
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France email: ammari@cmapx.polytechnique.fr, eunjoo@cmapx.polytechnique.fr, mklim@cmapx.polytechnique.fr
MIKYOUNG LIM
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France email: ammari@cmapx.polytechnique.fr, eunjoo@cmapx.polytechnique.fr, mklim@cmapx.polytechnique.fr
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Abstract

The notion of polarization tensor is employed for the derivation of the leading-order boundary perturbations in the steady-state voltage potentials that are due to the presence of conductivity inclusions of small diameter. Recently, Capdeboscq and Vogelius obtained optimal bounds of Hashin-Shtrikman type for the trace of the polarization tensor, showing that every pair satisfying these optimal bounds arises as the eigenvalues of a polarization tensor associated with a coated ellipse. In this paper, we give numerical evidence of the fact that the set of possible polarization tensor eigenvalue pairs can also be obtained using simply connected domains. Our numerical computations are based on a boundary integral method.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 17 , Issue 2 , April 2006 , pp. 201 - 219
Copyright
2006 Cambridge University Press

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