# Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area

Elena Beretta, Arup Mukherjee, Michael Vogelius

Research output: Contribution to journalArticle

### Abstract

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  for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

Original language English (US) 543-572 30 Zeitschrift fur Angewandte Mathematik und Physik 52 4 https://doi.org/10.1007/PL00001561 Published - Jan 1 2001

### Fingerprint

Imperfections
Asymptotic Formula
Conductivity
Voltage
conductivity
Defects
defects
Electric potential
electric potential
Integral equations
integral equations
Integral Equations
Two Dimensions
derivation
Cover
Curve
curves
Term

### Keywords

• Asymptotic formulas
• Inverse conductivity problem
• Thin imperfections

### ASJC Scopus subject areas

• Mathematics(all)
• Physics and Astronomy(all)
• Applied Mathematics

### Cite this

Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. / Beretta, Elena; Mukherjee, Arup; Vogelius, Michael.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 52, No. 4, 01.01.2001, p. 543-572.

Research output: Contribution to journalArticle

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N2 - 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  for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

AB - 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  for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

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