Determining an unbounded potential for an elliptic equation with a power type nonlinearity
Nurminen, J. (2023). Determining an unbounded potential for an elliptic equation with a power type nonlinearity. Journal of Mathematical Analysis and Applications, 523(1), Article 126962. https://doi.org/10.1016/j.jmaa.2022.126962
Published inJournal of Mathematical Analysis and Applications
© 2023 The Author(s). Published by Elsevier Inc.
In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential q in ��/2+�, �>0, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results from [LLLS21b] where this is shown for Hölder continuous potentials. Also we show that when the Dirichlet-to-Neumann map is restricted to one point on the boundary, it is possible to determine a potential q in ��+�. The authors of [ST22] proved this to be true for Hölder continuous potentials.
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Related funder(s)Academy of Finland
Funding program(s)Centre of Excellence, AoF
Additional information about fundingThe author was supported by the Finnish Centre of Excellence in Inverse Modelling and Imaging (Academy of Finland grant 284715).
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