An inverse problem for the fractional Schrödinger equation in a magnetic field
Covi, G. (2020). An inverse problem for the fractional Schrödinger equation in a magnetic field. Inverse Problems, 36(4), Article 045004. https://doi.org/10.1088/1361-6420/ab661a
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Inverse ProblemsAuthors
Date
2020Discipline
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsCopyright
© 2019 IOP Publishing Ltd
This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrödinger 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.
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Institute of PhysicsISSN Search the Publication Forum
0266-5611Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/33920490
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European CommissionFunding program(s)
ERC Consolidator Grant
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about funding
This work is part of the PhD research of the author, who was partially supported by the European Research Council under Horizon 2020 (ERC CoG 770924). The author wishes to express his sincere gratitude to Professor Mikko Salo for his reliable guidance and constructive discussion in the making of this work.License
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