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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.