A note on the shift theorem for the Laplacian in polygonal domains (extended version)
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913573479907328 |
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| author | Melenk, Jens Markus Rojik, Claudio |
| author_facet | Melenk, Jens Markus Rojik, Claudio |
| contents | We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the shift theorem for the Laplacian in polygonal domains (extended version) Melenk, Jens Markus Rojik, Claudio Analysis of PDEs 35J25, 35B6535J25, 35B65 35J25, 35B65 We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces. |
| title | A note on the shift theorem for the Laplacian in polygonal domains (extended version) |
| topic | Analysis of PDEs 35J25, 35B6535J25, 35B65 35J25, 35B65 |
| url | https://arxiv.org/abs/2409.17037 |