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A variational method for wave scattering from penetrable rough layers. (English) Zbl 1205.78024
The paper is devoted to time-harmonic wave scattering problems for infinite penetrable anisotropic layers in two or three dimensions within a variational approach. Due to non-trapping assumptions on the material parameters, the authors establish a priori bounds for the solutions of such problems through integral identities of the Rellich type. Existence and uniqueness of solution are obtained using a generalized Lax-Milgram theory. Additionally, a regularity theory for the rough-layer scattering problem and bounds on its frequency dependence are also derived.

78A45 Diffraction, scattering
78M30 Variational methods applied to problems in optics and electromagnetic theory
35P25 Scattering theory for PDEs
35A15 Variational methods applied to PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J20 Variational methods for second-order elliptic equations
78A40 Waves and radiation in optics and electromagnetic theory
78A48 Composite media; random media in optics and electromagnetic theory
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