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We consider the inverse problem of determining, the possibly anisotropic,conductivity of a body by means of the so called local Neumann to Dirichlet mapon a curved portion $\Sigma$ of the boundary. Motivated by the uniquenessresult for piecewise constant anisotropic conductivities proved in\cite{Al-dH-G}, we provide a H\"{o}lder stability estimate on $\Sigma$ when theconductivity is a priori known to be a constant matrix near $\Sigma$.

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