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On the fractional Sch\"odinger equation with variable coefficients

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arxiv 2411.01300 v1 pith:MCVB2CWH submitted 2024-11-02 math.AP

C. E. Kenig , D. Pilod , G. Ponce , L. Vega This is my paper · ORCID
classification math.AP
keywords fractionalcoefficientsvariableellipticequationodingeroperatorproblem
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We study the initial value problem (IVP) associated to the semi-linear fractional Sch\"odinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modelling the dispersion relation and use them to establish the local well-posedness for the corresponding IVP. Also, we obtain unique continuation results concerning the solutions of this problem. These are consequences of uniqueness properties that we prove for the fractional elliptic operator with variable coefficients

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Cited by 2 Pith papers

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    Exterior Dirichlet-to-Neumann data for fractional Laplace-Beltrami operators determine a Euclidean-asymptotic Riemannian metric up to a diffeomorphism fixing the exterior.

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    math.AP 2024-12 conditional novelty 7.0 of 10

    A unique-continuation principle for sums of fractional Laplacians is proved on Euclidean space and applied to recover anisotropic coefficients and potentials in fractional polyharmonic equations.

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