论文标题
关于小数calderón问题的单个测量稳定性
On Single Measurement Stability for the Fractional Calderón Problem
论文作者
论文摘要
在此简短的说明中，我们证明了在\ cite {grsu18}中得出的分数calderón问题的单个测量唯一性结果的对数稳定性。为此，我们使用在\ cite {rs20a}中建立的定量唯一性结果，并以边界加倍估计来补充这些边界。后者可以控制分数schrödinger方程消失的溶液的顺序。然后，在\ cite {s10，asv13}中引入的方案之后，在确定远场测量的表面阻抗的上下文中，这使我们能够推断出潜在$ q $的对数稳定性。
In this short note we prove the logarithmic stability of the single measurement uniqueness result for the fractional Calderón problem which had been derived in \cite{GRSU18}. To this end, we use the quantitative uniqueness results established in \cite{RS20a} and complement these bounds with a boundary doubling estimate. The latter yields control of the order of vanishing of solutions to the fractional Schrödinger equation. Then, following a scheme introduced in \cite{S10,ASV13} in the context of the determination of a surface impedance from far field measurements, this allows us to deduce logarithmic stability of the potential $q$.
