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Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem

Clair Poignard (2012)

ESAIM: Proceedings

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...

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