The higher order fractional Calderón problem for linear local operators : Uniqueness
Covi, G., Mönkkönen, K., Railo, J., & Uhlmann, G. (2022). The higher order fractional Calderón problem for linear local operators : Uniqueness. Advances in Mathematics, 399, Article 108246. https://doi.org/10.1016/j.aim.2022.108246
Julkaistu sarjassa
Advances in MathematicsPäivämäärä
2022Oppiaine
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsTekijänoikeudet
© 2022 Published by Elsevier Inc.
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 one can uniquely recover the coefficients of the PDO from the exterior Dirichlet-to-Neumann (DN) map associated to the perturbed FSE. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. Our study generalizes recent results for the zeroth and first order perturbations to higher order perturbations.
Julkaisija
ElsevierISSN Hae Julkaisufoorumista
0001-8708Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/104350313
Metadata
Näytä kaikki kuvailutiedotKokoelmat
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 ... -
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 ... -
Inverse problems for a fractional conductivity equation
Covi, Giovanni (Pergamon Press, 2020)This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, ... -
The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability
Kow, Pu-Zhao; Lin, Yi-Hsuan; Wang, Jenn-Nan (Society for Industrial & Applied Mathematics (SIAM), 2022)We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and ... -
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.