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

    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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