Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field. (13th March 2017)

• Record Type: Journal Article
• Authors: Bellassoued, Mourad
• Is Part Of: Inverse problems. Volume 33:Number 5(2017:May)
• Publication Date: 2017-03-13
• Subjects: inverses problems -- stability estimates -- Dirichlet-to-Neumann map -- Schrödinger equation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa5fc5
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper we consider the inverse problem of determining, on a compact Riemannian manifold, the electric potential or the magnetic field in a Schrödinger equation via Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schrödinger equation. We prove in dimension n ⩾ 2 that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the magnetic field and the electric potential and we establish Hölder-type stability.