On scattering behavior of corner domains with anisotropic inhomogeneities

TL;DR

This paper explores how anisotropic, inhomogeneous corner domains scatter waves, linking non-scattering to free boundary problems and proving that certain Lipschitz domains always scatter incident waves under specific conditions.

Contribution

It establishes a connection between anisotropic non-scattering phenomena and Bernoulli free boundary problems, providing new insights into wave scattering in Lipschitz domains.

Findings

Lipschitz but not $C^{1,eta}$ corners always scatter waves.

Connection between scattering behavior and free boundary problems.

Proves scattering for a broad class of anisotropic inhomogeneous media.

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.