Eric Bonnetier (Université de Grenoble-Alpes)
Localized large gradients in composite media and the Neumann-Poincaré operator.
In composite media, places where inhomogeneities are touching or close to touching are likely to be areas where the solutions of the governing elliptic differential equations present large gradients. This concentration phenomenon proves very interesting in many exciting applications, such as medical imaging, bio-sensing and optoelectronics. It is intimately related to the properties of the Neumann Poincaré operator, an integral operator that can be used as a tool to represent solutions to elliptic differential equations, and also appears in related phenomena of super-resolution and cloaking. In this talk, we describe how the blow up of the gradients can be inferred from the spectral properties of the Neumann-Poincaré operator. This is joint work with Faouzi Triki (Université Grenoble-Alpes).
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