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

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

2000-01-18

arxiv.org/abs/math/0001099v4

Mathematics

Analysis of PDEs

Final revision, to appear in the Duke Mathmematical Journal

Scientific paper

We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger
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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