A "milder" version of Calderón's inverse problem for anisotropic conductivities and partial data

  • El Maati Ouhabaz

    Université Bordeaux 1, Talence, France
A "milder" version of Calderón's inverse problem for anisotropic conductivities and partial data cover
Download PDF

A subscription is required to access this article.

Abstract

Given a general symmetric elliptic operator

we define the associated Dirichlet–to–Neumann (D-t-N) map with partial data, i.e., data supported in a part of the boundary. We prove positivity, -estimates and domination properties for the semigroup associated with this D-t-N operator. Given and of the previous type with bounded measurable coefficients and , we prove that if their partial D-t-N operators (with and replaced by and ) coincide for all , then the operators and , endowed with Dirichlet, mixed or Robin boundary conditions are unitary equivalent. In the case of the Dirichlet boundary conditions, this result was proved recently by Behrndt and Rohleder [6] for Lipschitz continuous coefficients. We provide a different proof, based on spectral theory, which works for bounded measurable coefficients and other boundary conditions.

Cite this article

El Maati Ouhabaz, A "milder" version of Calderón's inverse problem for anisotropic conductivities and partial data. J. Spectr. Theory 8 (2018), no. 2, pp. 435–457

DOI 10.4171/JST/201