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Reconstruction of thin conductivity imperfections. (English) Zbl 1047.35130

Summary: We consider the case of a uniform plane conductor containing a thin curve-like inhomogeneity of finite conductivity. In this article we prove that the imperfection can be uniquely determined from the boundary measurements of the first order correction term in the asymptotic expansion of the steady state voltage potential as the thickness goes to zero.

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
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[1] DOI: 10.1016/S0196-8858(02)00557-2 · Zbl 1040.78008 · doi:10.1016/S0196-8858(02)00557-2
[2] DOI: 10.1007/PL00001561 · Zbl 0974.78006 · doi:10.1007/PL00001561
[3] DOI: 10.1007/BF01766988 · Zbl 0731.31003 · doi:10.1007/BF01766988
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