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

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.

Cited by in corpus (4)

• Stability estimate for an inverse problem for the Schr{ö}dinger equation in a magnetic field with time-dependent coefficient
• Stability estimate for a partial data inverse problem for the convection-diffusion equation
• Uniqueness for time-dependent inverse problems with single dynamical data
• Stability estimate for the aligned magnetic field in a periodic quantum waveguide from dirichlet-to-neumann map