Carlos R. Mamani

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20152017

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math-ph2017

Influence of the bound states in the Neumann Laplacian in a thin waveguide

Carlos R. Mamani, Alessandra A. Verri

We study the Neumann Laplacian operator $- Δ_{Ω}^{N}$ restricted to a twisted waveguide $Ω$ . The goal is to find the effective operator when the diameter of $Ω$ tends to zero. However,…

math-ph2016

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

Alessandra A. Verri, Carlos R. Mamani

We study the Neumann Laplacian $- Δ^{N}$ restricted to a periodic waveguide. In this situation its spectrum $σ (- Δ^{N})$ presents a band structure. Our goal and strategy is to get spectr…

math-ph2015

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 $- Δ^{D}$ in a periodic waveguide $Ω$ . On the condition that $Ω$ is sufficiently thin, we show that its spectrum $σ (- Δ^{D})$ is absolutely cont…