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A remark on partial data inverse problems for semilinear elliptic equations


Authors: Katya Krupchyk and Gunther Uhlmann
Journal: Proc. Amer. Math. Soc. 148 (2020), 681-685
MSC (2010): Primary 35R30, 35J61
DOI: https://doi.org/10.1090/proc/14844
Published electronically: November 13, 2019
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Abstract: We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $ \mathbb{R}^n$, $ n\ge 2$, for a class of semilinear elliptic equations uniquely determines the nonlinearity.


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Additional Information

Katya Krupchyk
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
Email: katya.krupchyk@uci.edu

Gunther Uhlmann
Affiliation: Department of Mathematics, University of Washington Seattle, Washington 98195-4350; Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email: gunther@math.washington.edu

DOI: https://doi.org/10.1090/proc/14844
Received by editor(s): May 10, 2019
Published electronically: November 13, 2019
Additional Notes: The research of the first author was partially supported by the National Science Foundation (DMS 1815922).
The research of the second author was partially supported by NSF and a Si-Yuan Professorship of HKUST
Communicated by: Ryan Hynd
Article copyright: © Copyright 2019 American Mathematical Society