Global counterexamples to uniqueness for a Calderón problem with C k conductivities
Résumé
Let Ω ⊂ R n , n ≥ 3, be a fixed smooth bounded domain, and let γ be a smooth conductivity in Ω. Consider a non-zero frequency λ0 which does not belong to the Dirichlet spectrum of Lγ = -div(γ∇•).
Then, for all k ≥ 1, there exists an infinite number of pairs of non-isometric C k conductivities (γ1, γ2) on Ω, (see Definition 1.4), which are close to γ (see Definition 2.1) such that the associated DN maps at frequency λ0 satisfy Λ γ 1 ,λ 0 = Λ γ 2 ,λ 0 .
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