An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain

  • Mourad Choulli

    Université de Lorraine, Metz, France
  • Éric Soccorsi

    Aix-Marseille Université, Marseille, France

Abstract

We consider the inverse problem of determining the unknown function α:RR\alpha: \mathbb{R} \to \mathbb{R} from the DN map associated with the operator div (A(x,α(x3)))(A(x',\alpha (x_3))\nabla \cdot) acting in the infinite straight cylindrical waveguide Ω=ω×R\Omega =\omega \times \mathbb{R}, where ω\omega is a bounded domain of R2\mathbb{R}^2. Here A=(Aij(x))A=(A_{ij}(x)), x=(x,x3)Ωx=(x',x_3) \in \Omega, is a matrix-valued metric on Ω\Omega obtained by straightening a twisted waveguide. This inverse anisotropic conductivity problem remains generally open, unless the unknown function α\alpha is assumed to be constant. In this case we prove Lipschitz stability in the determination of α\alpha from the corresponding DN map. The same result remains valid upon substituting a suitable approximation of the DN map, provided the function α\alpha is sufficiently close to some {\it a priori} fixed constant.

Cite this article

Mourad Choulli, Éric Soccorsi, An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain. J. Spectr. Theory 5 (2015), no. 2, pp. 295–329

DOI 10.4171/JST/99