Conductivity interface problems. Part I: Small perturbations of an interface

Authors:
Habib Ammari, Hyeonbae Kang, Mikyoung Lim and Habib Zribi

Journal:
Trans. Amer. Math. Soc. **362** (2010), 2435-2449

MSC (2000):
Primary 35B30

DOI:
https://doi.org/10.1090/S0002-9947-09-04842-9

Published electronically:
December 16, 2009

MathSciNet review:
2584606

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We derive high-order terms in the asymptotic expansions of boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with -boundary. Our derivation is rigorous and based on layer potential techniques. The asymptotic expansion in this paper is valid for -perturbations and inclusions with extreme conductivities. It extends those already derived for small volume conductivity inclusions and leads us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the inclusion based on boundary measurements. We perform some numerical experiments using the algorithm to test its effectiveness.

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Additional Information

**Habib Ammari**

Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France

Email:
ammari@cmapx.polytechnique.fr

**Hyeonbae Kang**

Affiliation:
Department of Mathematical Sciences and RIM, Seoul National University, Seoul 151-747, Korea

Address at time of publication:
Department of Mathematics, Inha University, Incheon 402-751, Korea

Email:
hkang@math.snu.ac.kr, hbkang@inha.ac.kr

**Mikyoung Lim**

Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523

Address at time of publication:
Department of Mathematical Sciences, Korean Advanced Institute of Science and Technology, 335 Gwahangno (373-1 Gueseong-dong), Yuseong-gu, Daejeon 305-701, Korea

Email:
lim@math.colostate.edu, mklim@kaist.ac.kr

**Habib Zribi**

Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France

Address at time of publication:
Department of Mathematical Sciences, Korean Advanced Institute of Science and Technology, 335 Gwahangno (373-1 Gueseong-dong), Yuseong-gu, Daejeon 305-701, Korea

Email:
zribi@cmapx.polytechnique.fr

DOI:
https://doi.org/10.1090/S0002-9947-09-04842-9

Keywords:
Small perturbations,
interface problem,
full asymptotic expansions,
boundary integral method

Received by editor(s):
January 13, 2006

Received by editor(s) in revised form:
January 27, 2008

Published electronically:
December 16, 2009

Article copyright:
© Copyright 2009
American Mathematical Society