Stability Estimates for Coefficients of Magnetic Schrödinger Equation from Full and Partial Boundary Measurements

In this paper we establish a log log-type estimate which shows that in dimension n ≥ 3 the magnetic field and the electric potential of the magnetic Schrödinger equation depends stably on the Dirichlet to Neumann (DN) map even when the boundary measurement is taken only on a subset that is slightly larger than half of the boundary ∂Ω – a notion made more precise later. Furthermore, we prove that in the case when the measurement is taken on all of ∂Ω one can establish a better estimate that is of log-type.