Pith. sign in

REVIEW 3 cited by

A Reduction of the Fractional Calder\'on Problem to the Local Calder\'on Problem by Means of the Caffarelli-Silvestre Extension

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2305.04227 v2 pith:43EX3DG3 submitted 2023-05-07 math.AP

Giovanni Covi , Tuhin Ghosh , Angkana Rüland , Gunther Uhlmann This is my paper · ORCID
classification math.AP
keywords problemcalderlocaldatacaffarelli-silvestrecoefficientdirichlet-to-neumannextension
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We relate the (anisotropic) variable coefficient local and nonlocal Calder\'on problems by means of the Caffarelli-Silvestre extension. In particular, we prove that (partial) Dirichlet-to-Neumann data for the fractional Calder\'on problem in three and higher dimensions determine the (full) Dirichlet-to-Neumann data for the local Calder\'on problem. As a consequence, any (variable coefficient) uniqueness result for the local problem also implies a uniqueness result for the nonlocal problem. Moreover, our approach is constructive and associated Tikhonov regularization schemes can be used to recover the data. Finally, we highlight obstructions for reversing this procedure, which essentially consist of two one-dimensional averaging processes.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. An Inverse Obstacle Problem for the Fractional Schr\"odinger Equation

    math.AP 2026-07 accept novelty 6.0 of 10

    A countable family of scaled exterior measurements of the fractional Schrödinger obstacle problem determines the nonnegative potential throughout the domain.

  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).

  3. Anisotropic Calder\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$

    math.AP 2025-06 reject novelty 5.0 of 10

    The paper claims an anisotropic Calderon uniqueness theorem for a logarithmic Laplacian of order 2+, but the central Paley-Wiener argument is invalid.

Pith tools