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 $\text{div}(σ\nabla u)=0$, where the complex admittivity $σ$ is of the form $σ=A(\cdot,a(\cdot))$ in a domain $Ω\subset\mathbb{R}^n$, $n\ge3$. We establish boundary stability estimates for $σ$ 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.