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

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.

arXiv comment22 pages

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