Monotonicity-based inversion of the fractional schodinger equation II. General potentials and stability

Bastian Harrach, Yi Hsuan Lin

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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).

Original languageEnglish
Pages (from-to)402-436
Number of pages35
JournalSIAM Journal on Mathematical Analysis
Issue number1
StatePublished - 1 Jan 2020


  • Fractional inverse problem
  • Fractional Schrodinger equation
  • Lipschitz stability
  • Localized potentials
  • Loewner order
  • Monotonicity


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