Stable boundary determination of a complex anisotropic admittivity and its derivatives from a local Neumann-to-Dirichlet map

Abstract

We study the classical anisotropic Calderón problem associated to the elliptic equation $\text{div}(\sigma \nabla u)=0$, where the complex admittivity $\sigma$ is of the form $\sigma =A(\cdot ,a(\cdot ))$ in a domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 3$. We establish boundary stability estimates for $\sigma$ and its derivatives of arbitrary order from a local Neumann-to-Dirichlet map. Our results extend those of Comm. Partial Differential Equations, 34 (2009) from the real-valued conductivity setting to complex anisotropic admittivities.

arXiv comment8 pages