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Existence and uniqueness of the solution of Maxwell’s system in heterogeneous and non-smooth media. (Existence et unicité des solutions du système de Maxwell pour des milieux hétérogènes non réguliers.) (French. Abridged English version) Zbl 0942.78006

Summary: This note is devoted to the derivation of the existence and uniqueness of the solution to Maxwell’s system when the permeability and the permittivity matrix belong only to \(L^\infty\). We consider two types of boundary conditions: a perfect conductor condition and a Silver-Müller condition. The proof is based on the use of a convenient regularization of the electromagnetic field.

MSC:

78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
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