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An inverse problem for the magnetic Schrödinger operator on a half space with partial data

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  • In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schrödinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in W_{comp}^{1,\infty}(\overline{\mathbb{R}_{-}^3},\mathbb{R}^3)$, and the electric pontetial $q \in L_{comp}^{\infty}(\overline{\mathbb{R}_{-}^3},\mathbb{C})$ are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space.
    Mathematics Subject Classification: Primary: 35R30.

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