Work

Fractional anisotropic Calderón problem with external data

Year: 2025

Type: preprint

Abstract: In this paper, we solve the fractional anisotropic Calderón problem with external data in the Euclidean space, in dimensions two and higher, for smooth Riemannian metrics that agree with the Euclidean metric outside a compact set. Specifically, we prove that the knowledge of the partial exterior Dirichlet--to--Neumann map for the fractional Laplace-Beltrami operator, given on arbitrary open nonempty sets in the exterior of the domain in the Euclidean space, determines the Riemannian metric up to diffeomorphism, fixing the exterior. We provide two proofs of this result: one relies on the heat semigroup representation of the fractional Laplacian and a pseudodifferential approach, while the other is based on a variable-coefficient elliptic extension interpretation of the fractional Laplacian.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2502.00710

Authors: Feizmohammadi, Ali, Ghosh, Tuhin, Krupchyk, Katya, Rüland, Angkana, Sjöstrand, Johannes, Uhlmann, Gunther

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Washington, Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, G2659019386, Anisotropic Inverse Problems: Nonlocality, Nonlinearity, and High Frequencies, Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité, G6803667113

OpenAlex ID: W4407124015

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