JournalsaihpcVol. 37, No. 5pp. 1143–1166

The Calderón problem for quasilinear elliptic equations

  • Gunther Uhlmann

    Department of Mathematics, University of Washington, Box 354350 Seattle, WA 98195, USA
  • Claudio Muñoz

    CNRS and Departamento de Ingeniería Matemática DIM, Universidad de Chile, Chile
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Abstract

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.

Cite this article

Gunther Uhlmann, Claudio Muñoz, The Calderón problem for quasilinear elliptic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 5, pp. 1143–1166

DOI 10.1016/J.ANIHPC.2020.03.004