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The Calder\'on problem for the fractional Schr\"odinger equation

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arxiv 1609.09248 v3 pith:IK5THUNA submitted 2016-09-29 math.AP

Tuhin Ghosh , Mikko Salo , Gunther Uhlmann This is my paper · ORCID
classification math.AP
keywords equationproblemfractionalcalderexteriorglobalinversemeasurements
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abstract

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.

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  1. An inverse problem for the fractional Schr\"odinger equation in a magnetic field

    math.AP 2019-08 conditional novelty 7.0 of 10

    The Dirichlet-to-Neumann map for the fractional magnetic Schrödinger equation uniquely determines the magnetic and electric potentials up to a natural gauge.

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