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Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. (English) Zbl 0974.78006

Summary: We derive asymptotic formulas for two dimensional steady state voltage potentials associated with thin, “curve-like” conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formulas (rigorously) derived in [D. J. Cedio-Fengya, S. Moskow and M. S. Vogelius, Inverse Probl. 14, 553-595 (1998; Zbl 0916.35132)] for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

MSC:

78A30 Electro- and magnetostatics
78M35 Asymptotic analysis in optics and electromagnetic theory
35J25 Boundary value problems for second-order elliptic equations
35R30 Inverse problems for PDEs

Citations:

Zbl 0916.35132
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