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Around the Research of Vladimir Maz'ya II pp 337–363Cite as

Boundary Integral Methods for Periodic Scattering Problems

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Part of the book series: International Mathematical Series ((IMAT,volume 12))

Abstract

The paper is devoted to the scattering of a plane wave obliquelyilluminating a periodic surface. Integral equation methods lead to a systemof singular integral equations over the profile. Using boundary integral techniques, we study the equivalence of these equations to the electromagneticformulation, 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.

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Authors and Affiliations

  1. Weierstrass Institute of Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    Gunther Schmidt

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  1. Gunther Schmidt
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Correspondence to Gunther Schmidt .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College, Queen's Gate 180, London, SW7 2AZ, United Kingdom

    Ari Laptev

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Schmidt, G. (2010). Boundary Integral Methods for Periodic Scattering Problems. In: Laptev, A. (eds) Around the Research of Vladimir Maz'ya II. International Mathematical Series, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1343-2_16

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