论文标题
关于椭圆形边界价值问题的参数识别问题发散形式，第一部分：抽象框架
On parameter identification problems for elliptic boundary value problems in divergence form, Part I: An abstract framework
论文作者
论文摘要
部分微分方程的参数识别问题是反问题的重要子类。参数到状态的映射将感兴趣的参数映射到系统的PDE或系统状态的各个解决方案中，在（通常是非线性）正向操作员中扮演着核心角色。因此，人们对定义明确的性质和进一步的分析属性感兴趣，例如该操作员W.R.T.的连续性和不同性能。该参数以确保来自反问题理论的技术可以成功地应用于逆问题。在这项工作中，我们提出了一个通用功能分析框架，该框架适用于研究一类巨大的参数识别问题，包括各种椭圆边界值问题（以差异形式），以及Dirichlet，Neumann，Robin，Robin或混合边界条件。特别是，我们表明，在适当条件下，相应的参数到状态操作员满足了切向锥条件，这通常是用于数值解决方案技术的。该框架特别涵盖了媒介中的反向问题和Terahertz断层扫描中出现的逆问题。
Parameter identification problems for partial differential equations are an important subclass of inverse problems. The parameter-to-state map, which maps the parameter of interest to the respective solution of the PDE or state of the system, plays the central role in the (usually nonlinear) forward operator. Consequently, one is interested in well-definedness and further analytic properties such as continuity and differentiability of this operator w.r.t. the parameter in order to make sure that techniques from inverse problems theory may be successfully applied to solve the inverse problem. In this work, we present a general functional analytic framework suited for the study of a huge class of parameter identification problems including a variety of elliptic boundary value problems (in divergence form) with Dirichlet, Neumann, Robin or mixed boundary conditions. In particular, we show that the corresponding parameter-to-state operators fulfil, under suitable conditions, the tangential cone condition, which is often postulated for numerical solution techniques. This framework particularly covers the inverse medium problem and an inverse problem that arises in terahertz tomography.
