WIAS Preprint No. 1435, (2009)

Integral methods for conical diffraction



Authors

  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 31A10 35J05 35Q60 35K50 45F15 78A45

Keywords

  • Diffraction, periodic structure, integral equation method, oblique incidence, system of singular integral equations

Abstract

The paper is devoted to the scattering of a plane wave obliquely illuminating a periodic surface. Integral equation methods lead to a system of singular integral equations over the profile. Using boundary integral techniques we study the equivalence of these equations to the electromagnetic formulation, the existence and uniqueness of solutions under general assumptions on the permittivity and permeability of the materials. In particular, new results for materials with negative permittivity or permeability are established.

Appeared in

  • Around the Research of Vladimir Maz'ya II. Partial Differential Equations, A. Laptev, ed., 12 of International Mathematical Series, Springer Science+Business Media, New York [et al.], 2010, pp. 337--363 under the new title "Boundary integral methods for periodic scattering problems''.

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