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Abstract

We consider the inverse boundary value problem of determining the potential q in the equation $Δ u + q u = 0$ in $Ω \subset R^{n}$ , from local Cauchy data. A result of global Lipschitz stability is obtained in dimension $n ⩾ 3$ for potentials that are piecewise linear on a given partition of Ω. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation $Δ u + k^{2} c^{- 2} u = 0$ at fixed frequency k.

Keywords

Lipschitz stability Cauchy data Green’s function Full Waveform Inversion

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Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

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