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arXiv · 2512.18175

On scattering behavior of corner domains with anisotropic inhomogeneities: part II

Pu-Zhao Kow·Mikko Salo·Henrik Shahgholian
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Abstract

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 $\notin\pi\mathbb{Q}$ always produce nontrivial scattering for any incoming wave.

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Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian. 2025-12-20. On scattering behavior of corner domains with anisotropic inhomogeneities: part II. https://doi.org/10.1016/j.jmaa.2026.130630

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