6533b7dbfe1ef96bd126f7a3

RESEARCH PRODUCT

The Calderón problem for the fractional Schrödinger equation

Tuhin GhoshMikko SaloGunther Uhlmann

subject

Approximation propertyDimension (graph theory)35J10Disjoint sets01 natural sciences35J70Domain (mathematical analysis)inversio-ongelmatSchrödinger equationsymbols.namesakeMathematics - Analysis of PDEs0103 physical sciencesApplied mathematicsUniqueness0101 mathematicsMathematicsosittaisdifferentiaaliyhtälötNumerical AnalysisCalderón problemApplied Mathematics010102 general mathematicsInverse problem35R30approximation propertyBounded functionsymbolsinverse problem010307 mathematical physicsfractional Laplacianapproksimointi26A33Analysis

description

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.

yearjournalcountryeditionlanguage
2020-01-01
http://urn.fi/URN:NBN:fi:jyu-202003202485