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2018 Influence of bounded states in the Neumann Laplacian in a thin waveguide
Carlos R. Mamani, Alessandra A. Verri
Rocky Mountain J. Math. 48(6): 1993-2021 (2018). DOI: 10.1216/RMJ-2018-48-6-1993

Abstract

Let $-\Delta _\Omega ^N$ be the Neumann Laplacian operator restricted to a twisted waveguide $\Omega $. Our first goal is to find the effective operator when $\Omega $ is ``squeezed.'' However, since, in this process, there are divergent eigenvalues, we consider $-\Delta _\Omega ^N$ acting in specific subspaces of the initial Hilbert space. The strategy is interesting since we find different effective operators in each situation. In the case where $\Omega $ is periodic and sufficiently thin, we also obtain information regarding the absolutely continuous spectrum of $-\Delta _\Omega ^N$ (restricted to such subspaces) and the existence and location of band gaps in its structure.

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Carlos R. Mamani. Alessandra A. Verri. "Influence of bounded states in the Neumann Laplacian in a thin waveguide." Rocky Mountain J. Math. 48 (6) 1993 - 2021, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1993

Information

Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 06987237
MathSciNet: MR3879314
Digital Object Identifier: 10.1216/RMJ-2018-48-6-1993

Subjects:
Primary: 35J10
Secondary: 47F05, 81V99

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 6 • 2018
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