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 previously for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.
Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area / Beretta, Elena; A. MUCKERJEE AND M., Vogelius. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 52:(2001), pp. 543-572. [10.1007/PL00001561]