TY - JOUR
T1 - Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis
AU - Beretta, Elena
AU - Francini, Elisa
AU - Vogelius, Michael S.
N1 - Funding Information:
This work was partially supported by the National Science Foundation under grant DMS-00-72556. Corresponding author. E-mail address: [email protected] (M.S. Vogelius).
PY - 2003/10/1
Y1 - 2003/10/1
N2 - 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].
AB - 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].
KW - Asymptotic formulas
KW - Conductivity problem
KW - Thin inhomogeneities
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U2 - 10.1016/S0021-7824(03)00081-3
DO - 10.1016/S0021-7824(03)00081-3
M3 - Article
AN - SCOPUS:0142024082
SN - 0021-7824
VL - 82
SP - 1277
EP - 1301
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
IS - 10
ER -