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

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica “G. Castelnuovo”, Universita' di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italia, , , , , , IT

    A. Mukherjee & M. Vogelius

  2. Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, , , , , , US

    E. Beretta

Authors
  1. E. Beretta
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  2. A. Mukherjee
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  3. M. Vogelius
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Received: May 18, 1999; revised: January 30, 2000

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Beretta, E., Mukherjee, A. & Vogelius, M. Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. Z. angew. Math. Phys. 52, 543–572 (2001). https://doi.org/10.1007/PL00001561

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  • DOI: https://doi.org/10.1007/PL00001561

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