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Carleman estimates for the wave equation in heterogeneous media with non-convex interface

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Figure 1: The thin continuous lines represent the level curves of the convex function ρ
Figure 2: The orthogonal projection is well-defined in U , the tubular neighborhood (denoted in gray) of the interface Γ ∗ .
Figure 3: An example of flat interface, where ξ = 3. Here is used ρ(x, y) = |(x, y) − (5, −3)| 2
Figure 4: If the interface Γ ∗ is given by the dotted black line, we can take ρ as the square of the Minkowski functional of the domain bounded by the thin blue curve.

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