The inverse problem for the fractional conductivity equation: a survey

Giovanni Covi

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

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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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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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