论文标题
LP空间中的各种源条件
Variational source conditions in Lp-spaces
论文作者
论文摘要
我们提出和分析了Tikhonov正则化方法的变异源条件（VSC），该方法对Banach空间中的一般性不足的操作员方程进行了LP-Norm惩罚。我们的分析基于著名的Littlewood-Paley理论和（Rademacher）R-Bondedness的概念。根据这两种分析工具，我们根据条件稳定性估计值验证了所提出的VSC，并根据Triebel-Lizorkin型空间的真实解决方案的规律性要求。在本文的最后一部分中，开发的理论应用于椭圆形问题，并通过测量数据进行了测量数据，以重建LP设定中可能无限的扩散系数。通过VSC，获得了与LP-Norm惩罚的相关Tikhonov正则化的收敛速率。
We propose and analyze variational source conditions (VSC) for the Tikhonov regularization method with Lp-norm penalties for a general ill-posed operator equation in a Banach space. Our analysis is based on the use of the celebrated Littlewood-Paley theory and the concept of (Rademacher) R-boundedness. On the basis of these two analytical tools, we validate the proposed VSC under a conditional stability estimate and a regularity requirement of the true solution in terms of Triebel-Lizorkin-type spaces. In the final part of the paper, the developed theory is applied to an inverse elliptic problem with measure data for the reconstruction of possibly unbounded diffusion coefficients in the Lp-setting. By means of VSC, convergence rates for the associated Tikhonov regularization with Lp-norm penalties are obtained.
