The Calderón problem for the fractionalSchrödinger equation
Tuhin Ghosh, Mikko Salo, Gunther Uhlmann
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 [math] 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.
Topics & Concepts
MathematicsBounded functionUniquenessInverse problemDomain (mathematical analysis)Dimension (graph theory)Mathematical analysisInverseApplied mathematicsProperty (philosophy)Partial differential equationUniqueness theorem for Poisson's equationInverse scattering problemFeature (linguistics)Well-posed problemGeneralized inverseNumerical methods in inverse problemsMicrowave Imaging and Scattering AnalysisNonlinear Partial Differential Equations