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

22 Scopus citations

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

Keywords

  • Asymptotic formulas
  • Inverse conductivity problem
  • Thin imperfections

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