Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces
The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface, in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. ¶ To solve the Maxwell transmission problem, we embed Maxwell’s equations in...[Show more]
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