# 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 [3] 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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AU - Mukherjee, Arup

AU - Vogelius, Michael

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Y1 - 2001/1/1

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 [3] 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 [3] for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

KW - Asymptotic formulas

KW - Inverse conductivity problem

KW - Thin imperfections

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