In this work, we use monotonicity-based methods for the fractional Schrodinger equation with general potentials q ∈L∞(Ω) in a Lipschitz bounded open set Ω ⊂Rn in any dimension n ∈ N. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness result for the fractional Calderon problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Schrodinger equation, and we prove uniqueness and Lipschitz stability from finitely many measurements for potentials lying in an a priori known bounded set in a finite dimensional subset of L∞(Ω).
- Fractional inverse problem
- Fractional Schrodinger equation
- Lipschitz stability
- Localized potentials
- Loewner order