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
Julkaistu sarjassa
Inverse ProblemsTekijät
Päivämäärä
2020Oppiaine
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsTekijänoikeudet
© 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.
Julkaisija
Institute of PhysicsISSN Hae Julkaisufoorumista
0266-5611Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/33920490
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Euroopan komissioRahoitusohjelmat(t)
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.
Lisätietoja rahoituksesta
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.Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse (American Institute of Mathematical Sciences (AIMS), 2021)We prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that ... -
The higher order fractional Calderón problem for linear local operators : Uniqueness
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther (Elsevier, 2022)We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that ... -
Optimality of Increasing Stability for an Inverse Boundary Value Problem
Kow, Pu-Zhao; Uhlmann, Gunther; Wang, Jenn-Nan (Society for Industrial & Applied Mathematics (SIAM), 2021)In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger ... -
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities
Lu, Shuai; Salo, Mikko; Xu, Boxi (IOP Publishing, 2022)We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential ... -
Uniqueness in an inverse problem of fractional elasticity
Covi, Giovanni; de Hoop, Maarten; Salo, Mikko (The Royal Society, 2023)We study a nonlinear inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lamé parameters associated with a linear, isotropic fractional ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.