A note on the spectrum of the Neumann Laplacian in periodic waveguides

Abstract

We study the Neumann Laplacian $-{\Delta }^N$ restricted to a periodic waveguide. In this situation its spectrum $\sigma (-{\Delta }^N)$ presents a band structure. Our goal and strategy is to get spectral information from an analysis of the asymptotic behavior of these bands provided that the waveguide is sufficiently thin.

arXiv commentWe corrected some details about the analyticity of the eigenvalues. arXiv admin note: text overlap with arXiv:1508.02574

References in corpus (1)

• Absolute continuity in periodic thin tubes and strongly coupled leaky wires