We consider an electrically conducting medium with conductivity inhomogeneities in the form of sheets of thickness 2epsilon. In this setup we provide a rigorous derivation of the leading terms in the asymptotic expansion of the steady state boundary voltage potentials, as epsilon --> 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]
Asymptotic formulas for steady state potentials in the presence of thin conductivity inhomogeneities / Beretta, Elena; E., Francini; M., Vogelius. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 82:(2003), pp. 1277-1301. [10.1016/S0021-7824(03)00081-3]
Asymptotic formulas for steady state potentials in the presence of thin conductivity inhomogeneities
BERETTA, Elena;
2003
Abstract
We consider an electrically conducting medium with conductivity inhomogeneities in the form of sheets of thickness 2epsilon. In this setup we provide a rigorous derivation of the leading terms in the asymptotic expansion of the steady state boundary voltage potentials, as epsilon --> 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]I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
