Exact Boundary Controllability of Maxwell's Equations in Heterogeneous Media

Let Ω be a Lipschitz polyhedron, in the sense that Ω is a bounded, simply connected Lipschitz domain with piecewise plane boundary. We denote by Γ the boundary of Ω and by ν the unit outer normal vector on Γ. We suppose that Ω is occupied by an electromagnetic medium of piecewise constant electric permittivity ε and piecewise constant magnetic permeability μ. More precisely, we assume that there exists a partition P https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/inq_chapter11_139_1.tif"/> of Ω in a finite set of Lipschitz polyhedra Ω₁,⋯, Ω _J such that on each Ωj, ε = εj and μ = μ_j , where ε _j and μ_j are positive constants.