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
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Journal of Mathematical Analysis and ApplicationsDate
2023Copyright
© 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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0022-247XKeywords
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Academy of FinlandFunding program(s)
Centre of Excellence, AoF
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The author was supported by the Finnish Centre of Excellence in Inverse Modelling and Imaging (Academy of Finland grant 284715).License
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