6533b7defe1ef96bd1275d6b
RESEARCH PRODUCT
Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement
Gunther UhlmannMikko SaloAngkana RülandTuhin Ghoshsubject
Calderón problemFractional equations010102 general mathematicsSingle measurementDisjoint sets01 natural sciencesConstructivefunctional analysisNull setContinuationMathematics - Analysis of PDEsRegularization (physics)0103 physical sciencesApplied mathematics010307 mathematical physicsUniqueness0101 mathematicsfunktionaalianalyysiAnalysisMathematicsdescription
We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 |