Determine a Magnetic Schrödinger Operator with a Bounded Magnetic Potential from Partial Data in a Slab

Abstract

We study an inverse boundary value problem with partial data in an infinite slab in $$\mathbb {R}^{n}$$ , $$n\ge 3$$ , for the magnetic Schrodinger operator with bounded magnetic potential and electric potential. We show that the magnetic field and the electric potential can be uniquely determined, when the Dirichlet and Neumann data are given on either different boundary hyperplanes or on the same boundary hyperplanes of the slab. These generalize the results in Krupchyk et al. (Commun Math Phys 312:87–126, 2012), where the same uniqueness results were established when the magnetic potential is Lipschitz continuous. The proof is based on the complex geometric optics solutions constructed in Krupchyk and Uhlmann (Commun Math Phys 327:993–1009, 2014), which are special solutions to the magnetic Schrodinger equation with $$L^{\infty }$$ magnetic and electric potentials in a bounded domain.