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arXiv · 1702.04222

Lipschitz stability for a piecewise linear Schr\"{o}dinger potential from local Cauchy data

Giovanni Alessandrini·Maarten V. de Hoop·Romina Gaburro·Eva Sincich
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Abstract

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

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Giovanni Alessandrini, Maarten V. de Hoop, Romina Gaburro, Eva Sincich. 2017-02-14. Lipschitz stability for a piecewise linear Schr\"{o}dinger potential from local Cauchy data. https://arxiv.org/abs/1702.04222

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