Related papers: Stability estimate in an inverse problem for non-a…
We study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that…
We consider the inverse problem of determining the time and space dependent electromagnetic potential of the Schr\"odinger equation in a bounded domain of $\mathbb R^n$, $n\geq 2$, by boundary observation of the solution over the entire…
We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…
In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…
In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…
In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely,…
We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…
In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential or the magnetic field in a Schr\"odinger equation with Dirichlet data from measured Neumann boundary observations. This…
We study the inverse problem of determining a real-valued potential in the two-dimensional Schr\"odinger equation at negative energy from the Dirichlet-to-Neumann map. It is known that the problem is ill-posed and a stability estimate of…
We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…
In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the…
In this article, we study the boundary inverse problem of determining the aligned magnetic fiaeld appearing in the magnetic Schr\"odinger equation in a periodic quantum cylindrical waveguide. Provided that the Dirichlet-to-Neumann map of…
In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is…
In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and…
We consider the inverse problem of H\"oldder-stably determining the time- and space-dependent coefficients of the Schr\"odinger equation on a simple Riemannian manifold with boundary of dimension $n\geq2$ from knowledge of the…
We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…
We prove that the stationary magnetic potential vector and the electrostatic potential entering the dynamic magnetic Schr\"odinger equation can be Lipschitz stably retrieved through finitely many local boundary measurements of the solution.…
This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to Neumann map. We establish in…
In this paper we establish a global Carleman estimate for the fourth order Schr\"odinger equation posed on a $1-d$ finite domain. The Carleman estimate is used to prove the Lipschitz stability for an inverse problem consisting in retrieving…
We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schr\"odinger equation defined on an open bounded domain in $\mathbb{R}^n$, $n\geq 2$, with smooth enough boundary. We show that by…