Unique continuation property and poincaré inequality for higher order fractional laplacians with applications in inverse problems
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Date
2021-08Type
- Journal Article
Abstract
We prove a unique continuation property for the fractional Laplacian (−∆)s when s ∈ (−n/2, ∞) \ ℤ where n ≥ 1. In addition, we study Poincaré-type inequalities for the operator (−∆)s when s ≥ 0. We apply the results to show that one can uniquely recover, up to a gauge, electric and magnetic potentials from the Dirichlet-to-Neumann map associated to the higher order fractional magnetic Schrödinger equation. We also study the higher order fractional Schrödinger equation with singular electric potential. In both cases, we obtain a Runge approximation property for the equation. Furthermore, we prove a uniqueness result for a partial data problem of the d-plane Radon transform in low regularity. Our work extends some recent results in inverse problems for more general operators. Show more
Publication status
publishedExternal links
Journal / series
Inverse Problems and ImagingVolume
Pages / Article No.
Publisher
American Institute of Mathematical SciencesSubject
Fractional Laplacian; Fractional Poincaré inequality; Fractional Schrödinger equation; Inverse problems; Radon transform; Unique continuationMore
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