×

Reconstruction of thin conductivity imperfections. II: The case of multiple segments. (English) Zbl 1092.35115

[For part I, cf. ibid. 83, 63–76 (2004; Zbl 1047.35130).]
Summary: We consider the case of a uniform plane conductor containing multiple inhomogeneities that can be represented as neighborhoods of segments. We prove the Lipschitz continuous dependence of the segments from one boundary measurement of the steady state voltage potential.

MSC:

35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/BF00281494 · Zbl 0684.35087 · doi:10.1007/BF00281494
[2] DOI: 10.1088/0266-5611/14/3/011 · Zbl 0916.35132 · doi:10.1088/0266-5611/14/3/011
[3] DOI: 10.1137/S0036141001399234 · Zbl 1036.35050 · doi:10.1137/S0036141001399234
[4] DOI: 10.1016/S0196-8858(02)00557-2 · Zbl 1040.78008 · doi:10.1016/S0196-8858(02)00557-2
[5] Ammari H, Reconstruction of Small Inhomogeneities from Boundary Measurements 1846 (2004) · Zbl 1113.35148
[6] DOI: 10.1007/PL00001561 · Zbl 0974.78006 · doi:10.1007/PL00001561
[7] DOI: 10.1016/S0021-7824(03)00081-3 · doi:10.1016/S0021-7824(03)00081-3
[8] DOI: 10.1051/m2an:2003014 · Zbl 1137.35346 · doi:10.1051/m2an:2003014
[9] Capdeboscq Y, Contemporary Mathematics 362 pp 69– (2005)
[10] Bryan, K and Vogelius, M. A review of selected works on crack identification. Proceedings IMA Workshop on Geometric Methods in Inverse Problems and PDE Control. August2001. (To appear) · Zbl 1062.35166
[11] DOI: 10.1080/00036810310001620090 · Zbl 1047.35130 · doi:10.1080/00036810310001620090
[12] DOI: 10.1007/BF01766988 · Zbl 0731.31003 · doi:10.1007/BF01766988
[13] DOI: 10.1137/0118029 · Zbl 0211.19303 · doi:10.1137/0118029
[14] DOI: 10.1088/0266-5611/20/6/010 · Zbl 1077.35119 · doi:10.1088/0266-5611/20/6/010
[15] Colton D, Integral Equation Methods in Scattering Theory, Pure and Applied Mathematics (1983) · Zbl 0522.35001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.