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Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform

Allan Greenleaf·Gunther Uhlmann
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Abstract

We consider the Dirichlet-to-Neumann map associated to the Schrödinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potential over a two-plane is determined by the Cauchy data of certain exponentially growing solutions on any neighborhood of the intersection of the two-plane with the boundary.

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Allan Greenleaf, Gunther Uhlmann. 2000-11-09. Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform. https://arxiv.org/abs/math/0001099

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