Abboud, Toufic; Ammari, Habib Diffraction at a curved grating: TM and TE cases, homogenization. (English) Zbl 0865.35122 J. Math. Anal. Appl. 202, No. 3, 995-1026 (1996). A hierarchy of effective boundary conditions is derived for a Helmholtz equation with Dirichlet or Neumann boundary conditions. These generalized impedance boundary conditions approximate the effect of thin dielectric layers with perfectly conducting inclusions covering an object. The well-posed nature of the problem is established and error estimates are provided. Reviewer: A.Jeffrey (Newcastle upon Tyne) Cited in 24 Documents MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 78A25 Electromagnetic theory (general) Keywords:TM and TE modes; homogenization; Helmholtz equation; Dirichlet or Neumann boundary conditions; impedance boundary conditions; error estimates PDFBibTeX XMLCite \textit{T. Abboud} and \textit{H. Ammari}, J. Math. Anal. Appl. 202, No. 3, 995--1026 (1996; Zbl 0865.35122) Full Text: DOI