Tikhonov regularizations: New trends and recent developments

发布时间：2021-06-07 来源：赢咖3 浏览次数：

Speaker:	陈德汗	DateTime:	2021年6月6日（周日）下午14:00-14:50
Brief Introduction to Speaker: 陈德汗，赢咖3。		Place:	六号楼四楼会议室
Abstract:This talk presents the new trends and recent developments of Tikhonov regularizations in Hilbert and Banach settings. We first propose and analyze variational source conditions (VSC) for the Tikhonov regularization methods with Lp-penalties applied to an ill-posed operator equation in a Banach space. Our analysis is built on the celebrated Littlewood-Paley theory and the concept of (Rademacher) R-boundedness. With these two analytical principles, we validate the proposed VSC under a conditional stability estimate in terms of a dual Triebel-Lizorkin-type norm. On the other hand, we will presents the applications of VSCs in some inverse PDEs problems.