6533b851fe1ef96bd12aa1ea
RESEARCH PRODUCT
An inverse problem for the fractional Schrödinger equation in a magnetic field
Giovanni Covisubject
Electromagnetic fieldApproximation propertyApplied MathematicsMathematical analysis010103 numerical & computational mathematicsInverse problemRandom walk01 natural sciencesDomain (mathematical analysis)Computer Science ApplicationsTheoretical Computer ScienceSchrödinger equation010101 applied mathematicssymbols.namesakeBounded functionSignal ProcessingsymbolsUniqueness0101 mathematicsMathematical PhysicsMathematicsdescription
This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrodinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely many measurements of solutions taken in arbitrary open subsets of the exterior. The proof is based on Alessandrini's identity and the Runge approximation property, thus generalizing some previous works on the fractional Laplacian. Moreover, we show with a simple model that the FMSE relates to a long jump random walk with weights.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-02-26 | Inverse Problems |