Geodesic
Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem
Clair Poignard1
1 Team-Projet MC2, INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux, 351 cours de la Libération, F–3340 Talence, France
ESAIM. Proceedings, Tome 37 (2012), pp. 136-165 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be εα–periodic, ε being the magnitude of the mean thickness of the layer, and α a positive parameter describing the degree of roughness. For ε tending to zero, we determine the appropriate boundary layer correctors which lead to approximate transmission conditions equivalent to the effect of the rough thin layer. We also provide an explicit characterization of the polarization tensor as defined by Capdeboscq and Vogelius in [9]. The present paper revisits the previous works of the author [11, 13, 16, 17], and it also provides new results for the very rough case α > 1.
DOI : 10.1051/proc/201237004

Clair Poignard 1

1 Team-Projet MC2, INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux, 351 cours de la Libération, F–3340 Talence, France 
@article{EP_2012_37_a4,
     author = {Clair Poignard},
     title = {Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. {A} review for the conductivity problem},
     journal = {ESAIM. Proceedings},
     pages = {136--165},
     year = {2012},
     volume = {37},
     doi = {10.1051/proc/201237004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201237004/}
}
TY  - JOUR
AU  - Clair Poignard
TI  - Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem
JO  - ESAIM. Proceedings
PY  - 2012
SP  - 136
EP  - 165
VL  - 37
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201237004/
DO  - 10.1051/proc/201237004
LA  - en
ID  - EP_2012_37_a4
ER  - 
%0 Journal Article
%A Clair Poignard
%T Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem
%J ESAIM. Proceedings
%D 2012
%P 136-165
%V 37
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201237004/
%R 10.1051/proc/201237004
%G en
%F EP_2012_37_a4
Clair Poignard. Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem. ESAIM. Proceedings, Tome 37 (2012), pp. 136-165. doi: 10.1051/proc/201237004

Cité par Sources :