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The Calder\'{o}n problem for nonlocal parabolic operators: A new reduction from the nonlocal to the local

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arxiv 2308.09654 v1 pith:TZV5I6MM submitted 2023-08-18 math.AP

Ching-Lung Lin , Yi-Hsuan Lin , Gunther Uhlmann This is my paper · ORCID
classification math.AP
keywords nonlocalparaboliccalderlocalproblemarticledirichlet-to-neumannequation
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abstract

In this article, we investigate the Calder\'on problem for nonlocal parabolic equations, where we are interested to recover the leading coefficient of nonlocal parabolic operators. The main contribution is that we can relate both (anisotropic) variable coefficients local and nonlocal Calder\'on problem for parabolic equations. More concretely, we show that the (partial) Dirichlet-to-Neumann map for the nonlocal parabolic equation determines the (full) Dirichlet-to-Neumann map for the local parabolic equation. This article extends our earlier results [LLU22] by using completely different methods. Moreover, the results hold for any spatial dimension $n\geq 2$.

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Cited by 4 Pith papers

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

  1. Fractional anisotropic Calder\'on problem with external data

    math.AP 2025-02 conditional novelty 7.0 of 10

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

  2. Entanglement principle for the fractional Laplacian with applications to inverse problems

    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.

  3. The Calder\'on problem for the logarithmic Schr\"odinger equation

    math.AP 2024-12 conditional novelty 6.0 of 10

    For the logarithmic Schrödinger operator, the Dirichlet-to-Neumann map uniquely determines bounded potentials in arbitrary space dimension, and monotonicity gives a constructive reconstruction.

  4. Optimal Runge approximation for damped nonlocal wave equations and simultaneous determination results

    math.AP 2024-12 conditional novelty 6.0 of 10

    For damped nonlocal wave equations, equality of exterior measurements uniquely determines the damping coefficient and the potential (or nonlinearity).

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