The Calderón problem for quasilinear elliptic equations

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

paper · doi:10.48550/arxiv.1806.09586

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

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