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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.07440 |
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| _version_ | 1866908698071269376 |
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| author | Xiang, Jianli Hu, Guanghui |
| author_facet | Xiang, Jianli Hu, Guanghui |
| contents | We study time harmonic scattering problems in linear elasticity in $\mathbb{R}^{2}$. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission eigenvalues, the far field operator has a trivial kernel at every real frequency. Our approach relies on a special decomposition of the elastic Lamé operator and also provides an alternative idea for treating inverse elastic medium problems with a general polygonal support. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of the analytic continuation of elastic transmission eigenfunctions at rectangular corners Xiang, Jianli Hu, Guanghui Analysis of PDEs We study time harmonic scattering problems in linear elasticity in $\mathbb{R}^{2}$. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission eigenvalues, the far field operator has a trivial kernel at every real frequency. Our approach relies on a special decomposition of the elastic Lamé operator and also provides an alternative idea for treating inverse elastic medium problems with a general polygonal support. |
| title | Absence of the analytic continuation of elastic transmission eigenfunctions at rectangular corners |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.07440 |