2020/08/24 by Giovanni Covi, Keijo Mönkkönen, Jesse Railo +2 · 8 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Boundary value problem #Bounded function #Dirichlet distribution #Laplace operator #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Operator (biology) #Order (exchange) #Pure mathematics #Sobolev space #Spectral Theory in Mathematical Physics #Uniqueness #math.AP #msc:35R11 #msc:35R30
paper · pdf · doi:10.1016/j.aim.2022.108246
published in arXiv (Cornell University) 399, 108246 (Cornell University) · 21 pages
openalex publication_date 2020/08/24 · arxiv created 2022/01/13 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 order of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the 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.