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
Published inInverse Problems
DisciplineInversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematics
© 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.
PublisherInstitute of Physics
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Related funder(s)European Commission
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 fundingThis 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.
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