Determining an anisotropic conductivity by boundary measurements: Stability at the boundary

We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body Omega subset of R-n, n >= 3, by means of the so-called local Neumann-to-Dirichlet map on a curved portion Sigma of its boundary partial derivative Omega. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in Inverse Problems 33 (2018), 125013, we provide a H & ouml;lder stability estimate on Sigma when the conductivity is a-priori known to be a constant matrix near Sigma.

Automated summary

This paper considers the inverse problem of determining the conductivity of a possibly anisotropic body Ω, subset of R-n, by means of the local Neumann-to-Dirichlet map on a curved portion Σ of its boundary. Motivated by the uniqueness result for piecewise constant anisotropic conductivities, the paper provides a Hölder stability estimate on Σ when the conductivity is a priori known to be a constant matrix near Σ.