论文标题
关于反问题的不稳定机制
On instability mechanisms for inverse problems
论文作者
论文摘要
在本文中，我们提出了三种可鲁棒的不稳定性机制，用于线性和非线性反问题。所有这些都是基于强大的压缩属性（从奇异值或熵数界限的意义上），我们分别针对相应的前向操作员分别通过强大的全局平滑性，只有弱的全局平滑或微局部平滑。例如，作为应用程序，我们为唯一延续，向后热方程以及一般几何形状中的线性和非线性calderón类型问题提供了新的不稳定性论点，可能是在存在粗糙系数的情况下。在控制理论的背景下，我们的不稳定机制也可能引起人们的关注，从而估计了相当一般的环境中（近似）可控性的成本。这是文章的修订版``关于反问题的不稳定性机制''ARS Inveniendi Analytica（2021），同一作者的论文7，93 pp。
In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of singular value or entropy number bounds) which we deduce through either strong global smoothing, only weak global smoothing or microlocal smoothing for the corresponding forward operators, respectively. As applications we for instance present new instability arguments for unique continuation, for the backward heat equation and for linear and nonlinear Calderón type problems in general geometries, possibly in the presence of rough coefficients. Our instability mechanisms could also be of interest in the context of control theory, providing estimates on the cost of (approximate) controllability in rather general settings. This is a revised version of the article ``On instability mechanisms for inverse problems'' Ars Inveniendi Analytica (2021), Paper No. 7, 93 pp by the same authors.
