On scattering behavior of corner domains with anisotropic inhomogeneities

Abstract: This paper investigates the possible scattering and non-scattering behavior of an anisotropic and inhomogeneous Lipschitz medium at a fixed wave number and with a single incident field. We connect the anisotropic non-scattering problem to a Bernoulli type free boundary problem. By invoking methods from the theory of free boundaries, we show that an anisotropic medium with Lipschitz but not $C^{1,\alpha}$ boundary scatters every incident wave that satisfies a non-degeneracy condition.