AI 中文总结
该研究针对椭圆方程div(σ∇u)=0对应的经典各向异性Calderón问题，从局部Neumann-to-Dirichlet映射建立复各向异性电导率及其任意阶导数的边界稳定性估计，推广了2009年的相关研究成果。
AI 中文摘要
我们研究与椭圆方程div(σ∇u)=0相关的经典各向异性Calderón问题，其中复电导率σ在区域Ω⊂ℝⁿ（n≥3）中具有形式σ=A(·,a(·))。我们从局部Neumann-to-Dirichlet映射建立σ及其任意阶导数的边界稳定性估计，该结果将Comm. Partial Differential Equations 34卷（2009年）的研究从实值电导率情形推广到复各向异性电导率情形。
英文摘要
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.
Comments8 pages
