The higher order fractional Calderón problem for linear local operators: Uniqueness
By Giovanni Covi, Keijo Monkkonen, Jesse Railo, Gunther Uhlmann. Advances in Mathematics, 2020
65 citations recorded by the source corpus.
We study an inverse problem for the fractional Schrodinger 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.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/67db0916afd622d30f00aa5304a616c53afb1528
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In Computational Theory and Mathematics
- Katya Krupchyk
- Gunther Uhlmann
- Ali Feizmohammadi
- Tuhin Ghosh
- Mikko Salo
- Plamen Stefanov
- Matti Lassas
- Carlos E. Kenig
In Mathematical Physics
- Katya Krupchyk
- Gunther Uhlmann
- Tuhin Ghosh
- Ali Feizmohammadi
- Mikko Salo
- Yi-Hsuan Lin
- Plamen Stefanov
- Matti Lassas
Citations in the corpus
- Fractional anisotropic Calderón problem on closed Riemannian manifolds (2021, background): “Following this work, inverse problems of recovering lower order terms for fractional elliptic equations have been studied extensively, see for example [15], [14], [35], [34], [1], [4], [5], [6], [7], [8], [9], [30], [31], [33] for some of the important contributions.”