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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Inverse problems for the fractional-Laplacian with lower order non-local perturbations


Authors: S. Bhattacharyya, T. Ghosh and G. Uhlmann
Journal: Trans. Amer. Math. Soc. 374 (2021), 3053-3075
MSC (2020): Primary 35R30, 35R11
DOI: https://doi.org/10.1090/tran/8151
Published electronically: March 8, 2021
MathSciNet review: 4237942
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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.


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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.
Article copyright: © Copyright 2021 American Mathematical Society