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Explicit characterization of the polarization tensor for rough thin layers

Clair Poignard 1, 2 
2 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : In the paper ‘Approximate transmission conditions through a rough thin layer. The case of periodic roughness' (Eur. J. Appl. Math. 2010; 21: 51–75), Ciuperca et al. derive transmission conditions that are equivalent to a rough thin layer for the conductivity problem. These conditions involved a pair of vector fields (A0, a0) and two constants D1 and D2 that are given implicitly by solving a partial differential equation in the infinite strip × /2π. We give here an explicit expression of a0 in terms of A0, which shows that D1 equals zero. We infer an explicit characterization of the polarization tensor as given by Capdeboscq and Vogelius (ESAIM:M2AN. 2003; 37: 159–173).
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Submitted on : Tuesday, January 11, 2011 - 9:52:38 AM
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Clair Poignard. Explicit characterization of the polarization tensor for rough thin layers. European Journal of Applied Mathematics, Cambridge University Press (CUP), 2011, 22, pp.1-6. ⟨10.1017/S0956792510000252⟩. ⟨inria-00554686⟩



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