Fractional Laplacian in bended strip
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914169346850816 |
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| author | Bakharev, Fedor Matveenko, Sergey |
| author_facet | Bakharev, Fedor Matveenko, Sergey |
| contents | The spectral properties of the restricted fractional Laplacian with Dirichlet boundary conditions in a smoothly bent waveguide is investigated. The existence of eigenvalues below the threshold of the continuous spectrum is proved, generalizing classical results known for the local Laplace operator. Our approach utilizes the Caffarelli--Silvestre extension, addressing the specific geometric difficulties arising from the operator non-locality. The sufficient conditions on the curvature magnitude and distribution to ensure the existence of these trapped modes is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Laplacian in bended strip Bakharev, Fedor Matveenko, Sergey Spectral Theory 35R11, 81Q10 The spectral properties of the restricted fractional Laplacian with Dirichlet boundary conditions in a smoothly bent waveguide is investigated. The existence of eigenvalues below the threshold of the continuous spectrum is proved, generalizing classical results known for the local Laplace operator. Our approach utilizes the Caffarelli--Silvestre extension, addressing the specific geometric difficulties arising from the operator non-locality. The sufficient conditions on the curvature magnitude and distribution to ensure the existence of these trapped modes is established. |
| title | Fractional Laplacian in bended strip |
| topic | Spectral Theory 35R11, 81Q10 |
| url | https://arxiv.org/abs/2511.19296 |