On scattering behavior of corner domains with anisotropic inhomogeneities: part II
arXiv:2512.18175 · doi:10.1016/j.jmaa.2026.130630
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 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 obstacles with corners in two dimensions (and with edge points in higher dimensions) with angles always produce nontrivial scattering for any incoming wave.
22 pages