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Stability estimate for a semilinear elliptic inverse problem

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Abstract

We establish a logarithmic stability estimate for the inverse problem of determining the nonlinear term, appearing in a semilinear boundary value problem, from the corresponding Dirichlet-to-Neumann map. Our result can be seen as a stability inequality for an earlier uniqueness result by Isakov and Sylvester (Commun Pure Appl Math 47:1403–1410, 1994).

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Authors and Affiliations

  1. Université de Lorraine, 4 cours Léopold, 54052, Nancy cedex, France

    Mourad Choulli

  2. School of Mathematical Sciences, Nankai University, Tianjing, 300071, China

    Guanghui Hu

  3. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan

    Masahiro Yamamoto

  4. Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, no 54, 050094, Bucharest, Romania

    Masahiro Yamamoto

  5. People’s Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198, Moscow, Russian Federation

    Masahiro Yamamoto

Authors
  1. Mourad Choulli
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  2. Guanghui Hu
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  3. Masahiro Yamamoto
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Correspondence to Mourad Choulli.

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MC is supported by the Grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde). MY is supported by Grant-in-Aid for Scientific Research (S) 15H05740 of Japan Society for the Promotion of Science and by The National Natural Science Foundation of China (Nos. 11771270, 91730303). This work was supported by A3 Foresight Program“Modeling and Computation of Applied Inverse Problems” of Japan Society for the Promotion of Science and prepared with the support of the “RUDN University Program 5-100”

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Choulli, M., Hu, G. & Yamamoto, M. Stability estimate for a semilinear elliptic inverse problem. Nonlinear Differ. Equ. Appl. 28, 37 (2021). https://doi.org/10.1007/s00030-021-00704-9

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  • DOI: https://doi.org/10.1007/s00030-021-00704-9

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