Stability estimate for an inverse problem for the magnetic Schrodinger equation from the Dirichlet-to-Neumann map

摘要

We consider the problem of stability estimate of the inverse problem of determining the magnetic field entering the magnetic Schrodinger equation in a bounded smooth domain of R-n with input Dirichlet data, from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the solutions of the magnetic Schrodinger equation. We prove in dimension n >= 2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic Schrodinger equation measured on the boundary determines uniquely the magnetic field and we prove a Holder-type stability in determining the magnetic field induced by the magnetic potential.