On scattering behavior of corner domains with anisotropic inhomogeneities: part II
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910077393305600 |
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| author | Kow, Pu-Zhao Salo, Mikko Shahgholian, Henrik |
| author_facet | Kow, Pu-Zhao Salo, Mikko Shahgholian, Henrik |
| contents | We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024] and using free boundary techniques from [arXiv:2506.22328]. Our main results can be categorized into two distinct cases. In the first case, we show that in two dimensions, piecewise $C^{1}$ or convex penetrable obstacles with corners, and in higher dimensions, obstacles with edge points, always induce nontrivial scattering for any incoming wave. In the second case, we prove that piecewise $C^{1}$ obstacles with corners in two dimensions (and with edge points in higher dimensions) with angles $\notinπ\mathbb{Q}$ always produce nontrivial scattering for any incoming wave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On scattering behavior of corner domains with anisotropic inhomogeneities: part II Kow, Pu-Zhao Salo, Mikko Shahgholian, Henrik Analysis of PDEs 35J15, 35P25, 35R35 We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024] and using free boundary techniques from [arXiv:2506.22328]. Our main results can be categorized into two distinct cases. In the first case, we show that in two dimensions, piecewise $C^{1}$ or convex penetrable obstacles with corners, and in higher dimensions, obstacles with edge points, always induce nontrivial scattering for any incoming wave. In the second case, we prove that piecewise $C^{1}$ obstacles with corners in two dimensions (and with edge points in higher dimensions) with angles $\notinπ\mathbb{Q}$ always produce nontrivial scattering for any incoming wave. |
| title | On scattering behavior of corner domains with anisotropic inhomogeneities: part II |
| topic | Analysis of PDEs 35J15, 35P25, 35R35 |
| url | https://arxiv.org/abs/2512.18175 |