Uniqueness of the inverse scattering problem of a locally perturbed half-plane

In this paper, we consider the scattering problem by a locally perturbed half-plane,which can be reformulated as an exterior obstacle problem. However, the new obstacle is a bounded domain with nonsmooth boundary. By using the generalization of Greenʹs theorem to nonsmooth domain, we obtain that the obstacle is uniquely determined by the far field pattern.