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arXiv · 1006.0149

Stable determination of coefficients in the dynamical anisotropic Schr{ö}dinger equation from the Dirichlet-to-Neumann map

Mourad Bellassoued·David Dos Santos Ferreira
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Abstract

In this paper we are interested in establishing stability estimates in the inverse problem of determining on a compact Riemannian manifold the electric potential or the conformal factor in a Schrödinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension n bigger than 2 that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the electric potential and we establish Hölder-type stability estimates in determining the potential. We prove similar results for the determination of a conformal factor close to 1.

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Mourad Bellassoued, David Dos Santos Ferreira. 2010-06-01. Stable determination of coefficients in the dynamical anisotropic Schr{ö}dinger equation from the Dirichlet-to-Neumann map. https://doi.org/10.1088/0266-5611%2F26%2F12%2F125010

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