In this paper we study the variational method and integral equation methods for a conical diffraction problem for imperfectly conducting gratings modeled by the impedance boundary value problem of the Helmholtz equation in periodic structures. We justify the strong ellipticity of the sesquilinear form corresponding to the variational formulation and prove the uniqueness of solutions at any frequency. Convergence of the finite element method using the transparent boundary condition (Dirichlet-to-Neumann mapping) is verified. The boundary integral equation method is also discussed.

翻译：注意：英文专业词汇如“Helmholtz Equation”、“Dirichlet-to-Neumann mapping”等未进行翻译处理。