The Calderón problem for quasilinear elliptic equations

2018/06/25 by Claudio Muñoz, Gunther Uhlmann, Muñoz, Claudio +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1806.09586

27 pp

arxiv created 2018/06/25 · arxiv updated 2018/06/26

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 induces 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.

Cited by

• The Calderón Problem for Quasilinear Conductivities of Conformally Transversally Anisotropic Media
• Multi-parameter identification in systems of PDEs from internal data

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