Séminaire

Renata Bunoiu : "Homogenization of Materials with Sign Changing Coefficients"

abstract

Eric Bonnetier : "Homogenization of the eigenvalues of the Neumann-Poincaré operator"

We study the spectrum of the Neumann-Poincar\'e operator $K^\varepsilon$ of a periodic collection of smooth inhomogeneities, as the period $\varepsilon \to 0$. Under the assumption that the pattern of inhomogeneity is strictly included in the periodicity cell, we show that the limit set $\lim{\varepsilon \to 0} \sigma(K^_\varepsilon)$ is the union of a Bloch spectrum and of a boundary spectrum, associated with eigenfunctions which are not too small (as functions in $H^1$) near the boundary. As by-products, we obtain homogenization results for periodic media containing inclusions with negative conductivities.