On elastic scattering behavior of corner domains

Abstract

We investigate the scattering of elastic waves by anisotropic inhomogeneous media at a fixed wave number. We prove that, in two dimensions, every penetrable obstacle with piecewise $C^1$ boundary and corner singularities, and, in higher dimensions, every obstacle with edge singularities, scatters every incident wave satisfying suitable assumptions. This work extends our previous result [J. Math. Anal. Appl. 2026, doi:10.1016/j.jmaa.2026.130630] from scalar equations to systems of equations, a generalization that requires a more delicate blowup analysis and more involved computations. Roughly speaking, our results establish the principle that \emph{corners always scatter} for general anisotropic media with variable coefficients.

arXiv comment28 pages