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

Jessica Crosse; Romina Gaburro

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arXiv · 2608.18674

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

Jessica Crosse·Romina Gaburro

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Abstract

We study the classical anisotropic Calder\'on 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 $\Omega\subset\mathbb{R}^n$, $n\ge3$. 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.

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Jessica Crosse, Romina Gaburro. 2026-08-19. Stable boundary determination of a complex anisotropic admittivity and its derivatives from a local Neumann-to-Dirichlet map. https://arxiv.org/abs/2608.18674

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