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 by means of the so called local Neumann to Dirichlet map on a curved portion $\mathrm{\Sigma }$ of the boundary. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in \cite{Al-dH-G}, we provide a Hölder stability estimate on $\mathrm{\Sigma }$ when the conductivity is a priori known to be a constant matrix near $\mathrm{\Sigma }$.