Exponential instability in an inverse problem for the Schrodinger equation

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 the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are...

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Bibliographic Details
Main Author: N. Mandache
Format: Default Preprint
Published: 2001
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Other mathematical sciences not elsewhere classified
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Mathematical Sciences not elsewhere classified
Online Access:https://hdl.handle.net/2134/680
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Summary: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 the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are optimal.

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