The quasi-static plasmonic problem for polyhedra

Abstract

We characterize the essential spectrum of the plasmonic problem for polyhedra in ${\mathbb{R}}^3$. The description is particularly simple for convex polyhedra and permittivities $\epsilon <-1$. The plasmonic problem is interpreted as a spectral problem through a boundary integral operator, the direct value of the double layer potential, also known as the Neumann--Poincaré operator. We therefore study the spectral structure of the the double layer potential for polyhedral cones and polyhedra.

34 pages, 3 figures. To appear in Mathematische Annalen

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