Fractional Laplacian in V-shaped waveguide
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910460254617600 |
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| author | Bakharev, Fedor Matveenko, Sergey |
| author_facet | Bakharev, Fedor Matveenko, Sergey |
| contents | The spectral properties of the restricted fractional Dirichlet Laplacian in ${\sf V}$-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[Λ_\dagger, +\infty)$ with the threshold corresponding to the smallest eigenvalue of the cross-sectional problems. In this work the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Laplacian in V-shaped waveguide Bakharev, Fedor Matveenko, Sergey Spectral Theory Analysis of PDEs 35R11, 81Q10 The spectral properties of the restricted fractional Dirichlet Laplacian in ${\sf V}$-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[Λ_\dagger, +\infty)$ with the threshold corresponding to the smallest eigenvalue of the cross-sectional problems. In this work the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle. |
| title | Fractional Laplacian in V-shaped waveguide |
| topic | Spectral Theory Analysis of PDEs 35R11, 81Q10 |
| url | https://arxiv.org/abs/2405.16892 |