The Calderón problem for the fractional Schrödinger equation

Tuhin Ghosh, Mikko Salo, Gunther Uhlmann
2020 Analysis & PDE  
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 ≥ 1 and are based on a strong approximation property of the fractional equation that extends earlier work. This special
more » ... ature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calderón problem.
doi:10.2140/apde.2020.13.455 fatcat:2uiw4gucwbapze24njr4zhhrty