An inverse problem for a linear Schrödinger equation in the presence of inhomogeneities of small volumes | Zendy

Khelifi A. | Zendy

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An inverse problem for a linear Schrödinger equation in the presence of inhomogeneities of small volumes

Author(s) -

Khelifi A.

Publication year - 2008

Publication title -

zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 51

eISSN - 1521-4001

pISSN - 0044-2267

DOI - 10.1002/zamm.200700073

Subject(s) - boundary (topology) , inverse problem , boundary value problem , mathematics , mathematical analysis , stability (learning theory) , inverse , schrödinger equation , computer science , geometry , machine learning

In this paper we prove that the knowledge of the partial (on part of the boundary) dynamic boundary measurements for the Schrödinger equation on any open subset Γ of the boundary determines uniquely the potential. Using a global Carleman estimate, we also derive a stability result with appropriate norms provided that Γ satisfies a suitable geometrical condition.

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