In this paper, the authors consider the scattering problem for a locally perturbed half-plane, and try to use the boundary integral equation method to prove the existence and uniqueness of the solution to the direct scattering problem. By reflecting the domain about the x1-axis, the scattering problem can be reformulated as an exterior Dirichlet obstacle problem, and the symmetry domain has corners. Carefully analysing the compactness of the boundary integral operators, the authors obtain the exist...
