Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis

Elena Beretta, Elisa Francini, Michael S. Vogelius

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We consider an electrically conducting medium with conductivity inhomogeneities in the form of sheets of thickness 2E. In this setup we provide a rigorous derivation of the leading terms in the asymptotic expansion of the steady state boundary voltage potentials, as E→0. In the two-dimensional case our derivation confirms the results, heuristically obtained in [E. Beretta et al., Z. Angew. Math. Phys. 52 (2001) 543-572].

Original languageEnglish (US)
Pages (from-to)1277-1301
Number of pages25
JournalJournal des Mathematiques Pures et Appliquees
Volume82
Issue number10
DOIs
StatePublished - Oct 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Asymptotic formulas
  • Conductivity problem
  • Thin inhomogeneities

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