European Journal of Applied Mathematics

Table of Contents - February 2011 - Volume 22, Issue 01  

Papers

Explicit characterization of the polarization tensor for rough thin layers

C. POIGNARDa1

a1 INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux1, 351 cours de la Libération, F - 33405 Talence Cedex, France email: clair.poignard@inria.fr

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).

(Received March 08 2010)

(Revised August 09 2010)

(Accepted August 10 2010)

(Online publication December 22 2010)