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 languageEnglish (US)
Pages (from-to)543-572
Number of pages30
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume52
Issue number4
DOIs
StatePublished - Jan 1 2001

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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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