Monotonicity of discrete spectra of Dirichlet Laplacian in 3-dimensional layers
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914582957654016 |
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| author | Bakharev, Fedor Matveenko, Sergey |
| author_facet | Bakharev, Fedor Matveenko, Sergey |
| contents | We investigate monotonicity properties of eigenvalues of the Dirichlet Laplacian in polyhedral layers of fixed width. We establish that eigenvalues below the essential spectrum threshold monotonically depend on geometric parameters defining the polyhedral layer, generalizing previous results known for planar V-shaped waveguides and conical layers. Moreover, we demonstrate non-monotone spectral behavior arising from asymmetric geometric perturbations, providing an explicit example where unfolding the polyhedral layer unexpectedly leads to the emergence of discrete eigenvalues. The limiting behavior of eigenvalues as the geometric parameters approach critical configurations is also rigorously analyzed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonicity of discrete spectra of Dirichlet Laplacian in 3-dimensional layers Bakharev, Fedor Matveenko, Sergey Spectral Theory Analysis of PDEs Primary: 35J05, 81Q10, Secondary: 35K05, 60J65 We investigate monotonicity properties of eigenvalues of the Dirichlet Laplacian in polyhedral layers of fixed width. We establish that eigenvalues below the essential spectrum threshold monotonically depend on geometric parameters defining the polyhedral layer, generalizing previous results known for planar V-shaped waveguides and conical layers. Moreover, we demonstrate non-monotone spectral behavior arising from asymmetric geometric perturbations, providing an explicit example where unfolding the polyhedral layer unexpectedly leads to the emergence of discrete eigenvalues. The limiting behavior of eigenvalues as the geometric parameters approach critical configurations is also rigorously analyzed. |
| title | Monotonicity of discrete spectra of Dirichlet Laplacian in 3-dimensional layers |
| topic | Spectral Theory Analysis of PDEs Primary: 35J05, 81Q10, Secondary: 35K05, 60J65 |
| url | https://arxiv.org/abs/2508.12696 |