Curved nonlinear waveguides
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912327209582592 |
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| author | Baldelli, Laura Krejcirik, David |
| author_facet | Baldelli, Laura Krejcirik, David |
| contents | The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the essential spectrum is positive whenever the cross-section is circular and the tube is asymptotically straight, untwisted and non-trivially bent. Second, a Hardy-type inequality is derived for unbent and non-trivially twisted tubes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Curved nonlinear waveguides Baldelli, Laura Krejcirik, David Analysis of PDEs Mathematical Physics Spectral Theory The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the essential spectrum is positive whenever the cross-section is circular and the tube is asymptotically straight, untwisted and non-trivially bent. Second, a Hardy-type inequality is derived for unbent and non-trivially twisted tubes. |
| title | Curved nonlinear waveguides |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2312.10357 |