6533b837fe1ef96bd12a31cc
RESEARCH PRODUCT
The Calderón problem for the fractional Schrödinger equation with drift
Yi-hsuan LinYi-hsuan LinAngkana RülandAngkana RülandMihajlo CekićMihajlo Cekićsubject
osittaisdifferentiaaliyhtälötLogarithmSingularity theoryApplied MathematicsContext (language use)Inverse probleminversio-ongelmatDomain (mathematical analysis)Schrödinger equationsymbols.namesakeMathematics - Analysis of PDEsBounded functionsymbolsApplied mathematicsUniquenessAnalysisMathematicsdescription
We investigate the Calder\'on problem for the fractional Schr\"odinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does \emph{not} enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many \emph{generic} measurements is discussed. Here the genericity is obtained through \emph{singularity theory} which might also be interesting in the context of hybrid inverse problems. Combined with the results from \cite{GRSU18}, this yields a finite measurements constructive reconstruction algorithm for the fractional Calder\'on problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension $n\geq 1$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 |