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The inverse problem for the fractional conductivity equation: a survey

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arxiv 2408.14200 v1 pith:QOIEJKSL submitted 2024-08-26 math.AP

Giovanni Covi This is my paper · ORCID
classification math.AP
keywords fractionalproblemcalderconductivityequationinverseasksaspects
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The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse problem. In this review we collect some recent results related to the conductivity formulation of the fractional Calder\'on problem.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometrical optics for the fractional Helmholtz equation and applications to inverse problems

    math.AP 2024-12 conditional novelty 8.0 of 10

    Fractional Helmholtz operators admit high-frequency geometrical optics solutions, and for s≥1/2 these give Hölder stable recovery of the potential from multi-frequency boundary Cauchy data.

  2. Partial data stability for the inverse fractional conductivity problem

    math.AP 2025-05 conditional novelty 6.0 of 10

    Partial exterior measurements stably determine the fractional conductivity, with logarithmic (resp. log-log) stability when conductivities agree in the exterior (resp. when their difference has compact support).

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