Stability Estimates for Coefficients of Magnetic Schrödinger Equation From Full and Partial Boundary Measurements
Leo Tzou
Abstract
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. 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. The proofs involve the use of the complex geometric optics (CGO) solutions of the magnetic Schrödinger equation constructed in sun uhlmann then follow a similar line of argument as in alessandrini. In the partial data estimate we follow the general strategy of hw by using the Carleman estimate established in FKSU and a continuous dependence result for analytic continuation developed in vessella.
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