Startseite Mathematik Determining both leading coefficient and source in a nonlocal elliptic equation
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Determining both leading coefficient and source in a nonlocal elliptic equation

  • Yi-Hsuan Lin ORCID logo EMAIL logo
Veröffentlicht/Copyright: 13. Januar 2025

Abstract

In this short note, we investigate an inverse (source) problem associated with a nonlocal elliptic equation ( - σ ) s u = F that is given in a bounded open set Ω n , for n 3 and 0 < s < 1 . We demonstrate both the leading coefficient σ and the source F can be determined uniquely by using the exterior Dirichlet-to-Neumann (DN) map in Ω e := n Ω ¯ . The result is intriguing in that analogous theory cannot be true for the local case generally, that is, s = 1 . The key ingredients to prove the uniqueness are based on the unique continuation principle for nonlocal elliptic operators and the reduction from the nonlocal to the local via the Stinga–Torrea extension problem.

MSC 2020: 35R30; 26A33; 35J70

Award Identifier / Grant number: 112-2628-M-A49-003

Award Identifier / Grant number: 113-2628-M-A49-003

Funding statement: Yi-Hsuan Lin is partially supported by the National Science and Technology Council (NSTC) Taiwan, under the projects 112-2628-M-A49-003 and 113-2628-M-A49-003. Yi-Hsuan Lin is also a Humboldt research fellowship for experienced researchers.

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Received: 2024-08-20
Revised: 2024-10-24
Accepted: 2024-11-11
Published Online: 2025-01-13
Published in Print: 2025-04-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 29.1.2026 von https://www.degruyterbrill.com/document/doi/10.1515/jiip-2024-0059/pdf
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