Geodesic
On asymptotic formula for electric resistance of conductor with small contacts
Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 15-27

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We construct and justify rigorously the complete asymptotic expansion for the electric resistance of a three-dimensional resistance connected by two small contacts of arbitrary shape. We obtain explicit formulae for the first two terms in the asymptotics generalized the classical Helm formula of one-term asymptotics for two small round contacts of same radius.
Keywords: electrical resistance, small contacts, Helm formula, asymptotic expansion, boundary value problem, the method of matching asymptotic expansions, mixed problem.
Mots-clés : Laplace equation 
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     title = {On asymptotic formula for electric resistance of conductor with small contacts},
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R. R. Gadylshin; A. A. Ershov; S. V. Repyevsky. On asymptotic formula for electric resistance of conductor with small contacts. Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 15-27. http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a2/