Stability estimate for a semilinear elliptic inverse problem

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). © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Authors
Choulli M. 1 , Hu G. 2 , Yamamoto M. 3, 4, 5
Journal
Nonlinear Differential Equations and Applications
Publisher
Birkhauser Verlag AG
Issue number
4
Language
English
State
Published
Link
External link
DOI
10.1007/S00030-021-00704-9
Number
37
Volume
28
Year
2021
Organizations
  • 1 Université de Lorraine, 4 cours Léopold, Nancy cedex, 54052, France
  • 2 School of Mathematical Sciences, Nankai University, Tianjing, 300071, China
  • 3 Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan
  • 4 Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, no 54, Bucharest, 050094, Romania
  • 5 People’s Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Keywords
Dirichlet-to-Neumann map; Semilinear elliptic BVP; Stability inequality
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