Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides

Carlos R. Mamani, Alessandra A. Verri

Consider the Dirichlet Laplacian operator $-{\Delta }^D$ in a periodic waveguide $\Omega$. On the condition that $\Omega$ is sufficiently thin, we show that its spectrum $\sigma (-{\Delta }^D)$ is absolutely cont…