On the growth properties of interior transmission eigenfunctions near corners
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914177644232704 |
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| author | Blåsten, Emilia L. K. Pohjola, Valter |
| author_facet | Blåsten, Emilia L. K. Pohjola, Valter |
| contents | We investigate the localization and vanishing of $L^2$ interior transmission eigenfunctions at corners. Past numerical computations suggest that these eigenfunctions localize at non-convex corners. This phenomenon has, however, not been proven theoretically. We show that localization does indeed occur for some eigenfunctions at a non-convex corner.
We also investigate the vanishing of interior transmission eigenfunctions at a convex corner. We prove that these eigenfunctions vanish at convex corners with reduced smoothness assumptions compared to earlier results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the growth properties of interior transmission eigenfunctions near corners Blåsten, Emilia L. K. Pohjola, Valter Analysis of PDEs Spectral Theory 35P25, 58J50, 35R30 We investigate the localization and vanishing of $L^2$ interior transmission eigenfunctions at corners. Past numerical computations suggest that these eigenfunctions localize at non-convex corners. This phenomenon has, however, not been proven theoretically. We show that localization does indeed occur for some eigenfunctions at a non-convex corner. We also investigate the vanishing of interior transmission eigenfunctions at a convex corner. We prove that these eigenfunctions vanish at convex corners with reduced smoothness assumptions compared to earlier results. |
| title | On the growth properties of interior transmission eigenfunctions near corners |
| topic | Analysis of PDEs Spectral Theory 35P25, 58J50, 35R30 |
| url | https://arxiv.org/abs/2512.02819 |