论文标题
反向电导率问题的稳定性估计值
Stability estimates for the inverse fractional conductivity problem
论文作者
论文摘要
我们研究了有界平滑域上分数电导率方程的反问题的稳定性。我们在适当的a在全球定义的电导率上获得了相反问题的对数稳定性估计。该论点具有三种主要成分：1。卢兰德和萨洛（Rüland）和萨洛（Rüland）和萨洛（Salo）的分数schrödinger方程相关问题的对数稳定性； 2。外部确定问题的Lipschitz稳定性； 3。利用和识别亚历山德里尼在经典calderón问题稳定性方面的非局部类比。本文的主要贡献是解决与上一步相关的技术困难的解决方案。此外，我们显示了对数稳定性估计值的最佳性，遵循Mandache对反电导率问题不稳定的早期作品，以及Rüland和Salo对分数Schrödinger方程的类似问题。
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined conductivities. The argument has three main ingredients: 1. the logarithmic stability of the related inverse problem for the fractional Schrödinger equation by Rüland and Salo; 2. the Lipschitz stability of the exterior determination problem; 3. utilizing and identifying nonlocal analogies of Alessandrini's work on the stability of the classical Calderón problem. The main contribution of the article is the resolution of the technical difficulties related to the last mentioned step. Furthermore, we show the optimality of the logarithmic stability estimates, following the earlier works by Mandache on the instability of the inverse conductivity problem, and by Rüland and Salo on the analogous problem for the fractional Schrödinger equation.
