Comptes Rendus
no. 3
Recovery of small electromagnetic inhomogeneities from partial boundary measurements
[Identification de petites inhomogénéités diélectriques à partir de mesures partielles]
Habib Ammari1 ; Alexander G. Ramm2
1 Centre de mathématiques appliquées, CNRS UMR 7641 & École polytechnique, 91128 Palaiseau cedex, France
2 Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA
Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 199-205.
corrigé par Erratum entitled: Recovery of small electromagnetic inhomogeneities from partial boundary measurements published in Série IIb, t. 330, n∘ 3, pp. 199–205

Nous considérons deux problèmes d'identification de petites inhomogénéités diélectriques à partir de mesures incomplètes. Pour chaque problème, nous construisons une fonction dont la transformée de Fourier inverse permet de localiser les petites inhomogénéités.

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(02)01449-3
Keywords: continuum mechanics, Helmholtz equation, reconstruction problem, small dielectric inhomogeneities, partial measurements
Mot clés : milieux continus, équation de Holmholtz, problème de reconstruction, petites inhomogénéités diélectriques, mesures partielles
Habib Ammari 1 ; Alexander G. Ramm 2

1 Centre de mathématiques appliquées, CNRS UMR 7641 & École polytechnique, 91128 Palaiseau cedex, France
2 Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA 
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Habib Ammari; Alexander G. Ramm. Recovery of small electromagnetic inhomogeneities from partial boundary measurements. Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 199-205. doi : 10.1016/S1631-0721(02)01449-3. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01449-3/

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[3] J. Sylvester; G. Uhlmann A global uniqueness theorem for an inverse boundary value problem, Ann. Math., Volume 125 (1987), pp. 153-169

[4] D. Isaacson; E.L. Isaacson Comments on Calderón's paper: “On an inverse boundary value problem”, Math. Compt., Volume 52 (1989), pp. 553-559

[5] H. Ammari, S. Moskow, M. Vogelius, Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter, ESAIM: Cont. Opt. Calc. Var., to appear

[6] H. Ammari, An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume, SIAM J. Control Optim., to appear

[7] R. Kohn; M. Vogelius Determining conductivity by boundary measurements, Comm. Pure Appl. Math., Volume 37 (1984), pp. 289-298

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