Inverse problems for the fractional-Laplacian with lower order non-local perturbations
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- by S. Bhattacharyya, T. Ghosh and G. Uhlmann PDF
- Trans. Amer. Math. Soc. 374 (2021), 3053-3075 Request permission
Abstract:
In this article, we introduce a model featuring a Lévy process in a bounded domain with semi-transparent boundary, by considering the fractional Laplacian operator with lower order non-local perturbations. We study the wellposedness of the model, certain qualitative properties and Runge type approximation. Furthermore, we consider the inverse problem of determining the unknown coefficients in our model from the exterior measurements of the corresponding Cauchy data. We also discuss the recovery of all the unknown coefficients from a single measurement.References
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Additional Information
- S. Bhattacharyya
- Affiliation: Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong
- MR Author ID: 1273208
- ORCID: 0000-0002-7467-7968
- Email: arkatifr@gmail.com
- T. Ghosh
- Affiliation: Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong; and Department of Mathematics, University of Washington
- Email: imaginetuhin@gmail.com
- G. Uhlmann
- Affiliation: Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong; and Department of Mathematics, University of Washington
- MR Author ID: 175790
- Email: gunther@math.washington.edu
- Received by editor(s): January 1, 2019
- Received by editor(s) in revised form: September 6, 2019, November 6, 2019, and February 14, 2020
- Published electronically: March 8, 2021
- Additional Notes: The first and second authors were partly supported by Project no. 16305018 of the Hong Kong Research Grant Council.
The third author was partly supported by NSF, the Si-Yuan Professorship at the IAS-HKUST and the Walker Family Endowed Professorship at the University of Washington. - © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 3053-3075
- MSC (2020): Primary 35R30, 35R11
- DOI: https://doi.org/10.1090/tran/8151
- MathSciNet review: 4237942