The Calderón problem for quasilinear elliptic equations
Muñoz, Claudio1 ; Uhlmann, Gunther2
1 CNRS and Departamento de Ingeniería Matemática DIM, Universidad de Chile, Chile
2 Department of Mathematics, University of Washington, Box 354350 Seattle, WA 98195, USA
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1143-1166.
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In this paper we show uniqueness of the conductivity for the quasilinear Calderón's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induce a unique Dirichlet-to-Neumann (DN) map. The method of proof considers some complex-valued, linear test functions based on a point of the boundary of the domain, and a linearization of the DN map placed at these particular set of solutions.

DOI : 10.1016/j.anihpc.2020.03.004
Classification : 35R30, 35J62
Mots-clés : Calderón problem, Inverse problem, Quasilinear conductivity
Muñoz, Claudio 1 ; Uhlmann, Gunther 2

1 CNRS and Departamento de Ingeniería Matemática DIM, Universidad de Chile, Chile
2 Department of Mathematics, University of Washington, Box 354350 Seattle, WA 98195, USA 
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Muñoz, Claudio; Uhlmann, Gunther. The Calderón problem for quasilinear elliptic equations. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1143-1166. doi : 10.1016/j.anihpc.2020.03.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.03.004/

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