Vol. 13, No. 2, 2020

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The Calderón problem for the fractional Schrödinger equation

Tuhin Ghosh, Mikko Salo and Gunther Uhlmann

Vol. 13 (2020), No. 2, 455–475
Abstract

We show global uniqueness in an inverse problem for the fractional Schrödinger 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 measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\ge 1$ 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 Calderón problem.

Keywords
inverse problem, Calderón problem, fractional Laplacian, approximation property
Mathematical Subject Classification 2010
Primary: 26A33, 35J10, 35R30
Secondary: 35J70