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

Victor Isakov | Zendy

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

Author(s) -

Victor Isakov

Publication year - 2010

Publication title -

discrete and continuous dynamical systems - s

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 34

eISSN - 1937-1632

pISSN - 1937-1179

DOI - 10.3934/dcdss.2011.4.631

Subject(s) - a priori and a posteriori , dirichlet distribution , stability (learning theory) , mathematical proof , von neumann architecture , mathematics , dirichlet problem , schrödinger equation , schrödinger's cat , energy (signal processing) , mathematical analysis , pure mathematics , computer science , geometry , boundary value problem , machine learning , philosophy , statistics , epistemology

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 Schrodinger 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.

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