Exponential instability in an inverse problem for the Schrodinger equation

By N. Mandache. 2001

310 citations recorded by the source corpus.

We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrodinger operator. We show that this problem is severely ill-posed. The results extend to electrical impedance tomography. They show that the logarithmic stability results of Alessandrini are optimal (up to the value of the exponent).

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/81f0f1d7d93041bf771e49c7601aff0e7b17cdb6

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In Biomedical Engineering

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids (2005, result): “However, distinguis hability grids are constructed with a linearization, heuristic approach, and rigo rous answers to the question of optimal parametrization of σ have yet to be found in general, although there are some new, promising results in this direction [59, 58] that are reminiscent of stabil”
Inverse problems: seeing the unseen (2014, background): “Mandache [127] has shown that this estimate is optimal up to the value of the exponent.”
Stability of Calderón inverse conductivity problem in the plane (2007, background): “Mandache [28] shows that even for C∞ conductivities this is the best one can expect.”
Electrical impedance tomography and Calderón's problem (2009, background): “Mandache [87] has shown that this estimate is optimal up to to the value of the exponent.”
Recent progress in electrical impedance tomography (2003, background): “In fact, it is severely ill-posed by all known measuring scales, cf [1, 15, 28 ].”