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

Abstract

In this paper we establish a $loglog$-type estimate which shows that in dimension $n\ge 3$ 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 $\partial \Omega$. Furthermore, we prove that in the case when the measurement is taken on all of $\partial \Omega$ one can establish a better estimate that is of $log$-type. The proofs involve the use of the complex geometric optics (CGO) solutions of the magnetic Schrödinger equation constructed in \cite{sun uhlmann} then follow a similar line of argument as in \cite{alessandrini}. In the partial data estimate we follow the general strategy of \cite{hw} by using the Carleman estimate established in \cite{FKSU} and a continuous dependence result for analytic continuation developed in \cite{vessella}.

Cited by in corpus (1)

• Inverse boundary value problems for the magnetic Schroedinger equation