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.

arXiv comment34 pages, 3 figures. To appear in Mathematische Annalen

References in corpus (4)

• Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples
• The essential spectrum of the Neumann--Poincare operator on a domain with corners
• Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum
• The transmission problem on a three-dimensional wedge

Cited by in corpus (2)

• Maxwell's equations with hypersingularities at a negative index material conical tip
• Infinitely many embedded eigenvalues for the Neumann-Poincaré operator in 3D