Beretta, Elena; Mukherjee, Arup; Vogelius, Michael Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. (English) Zbl 0974.78006 Z. Angew. Math. Phys. 52, No. 4, 543-572 (2001). 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. Cited in 1 ReviewCited in 13 Documents 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 Keywords:inverse conductivity; thin imperfections; asymptotic formulas Citations:Zbl 0916.35132 PDFBibTeX XMLCite \textit{E. Beretta} et al., Z. Angew. Math. Phys. 52, No. 4, 543--572 (2001; Zbl 0974.78006) Full Text: DOI