A1 Journal article (refereed)
The higher order fractional Calderón problem for linear local operators : Uniqueness (2022)

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

JYU authors or editors

Publication details

All authors or editors: Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther

Journal or series: Advances in Mathematics

ISSN: 0001-8708

eISSN: 1090-2082

Publication year: 2022

Volume: 399

Article number: 108246

Publisher: Elsevier

Publication country: Netherlands

Publication language: English

DOI: https://doi.org/10.1016/j.aim.2022.108246

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/79921

Publication is parallel published: https://arxiv.org/abs/2008.10227

Abstract

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.

Keywords: partial differential equations; inverse problems

Free keywords: Fractional Calderón problem; Fractional Schrödinger equation; Sobolev multipliers

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 3