讲座摘要

This talk presents the new trends and recent developments of Tikhonov regularizations in Hilbert and Banach settings, which is one of the major tools to obtain stable approximations of ill-posed problems. In particular, we propose and analyze variational source conditions (VSC) for the Tikhonov regularization method 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. Some applications in parameter identification are given.

个人简介

陈德汗，华中师范大学讲师，2010年和2013获得南昌大学学士和硕士研究生学位，2016年获得香港中文大学博士学位。2017-2018年获得德国洪堡基金。陈德汗博士的研究领域包括偏微分方程反问题、正则化方法和抽象发展方程等，主持国家自然科学基金项目1项，在SIAM Journal on Mathematical Analysis, M3AS, Journal of Functional analysis, Journal of Differential Equations, Inverse Problems, Inverse Problems and Imagining等国际知名刊物上发表论文近20篇。