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Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map

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  • We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovery of the potential coefficient in the Schrödinger equation from the Dirichlet-to-Neumann map, when frequency (energy level) is growing. These bounds hold under certain a-priori bounds on the unknown coefficient. Proofs use complex- and real-valued geometrical optics solutions. We outline open problems and possible future developments.
    Mathematics Subject Classification: Primary: 35R30; Secondary: 78A46.

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