时间地点：2020年12月8日，下午2:30-3:30
腾讯会议 ID：930 8501 3797，会议密码：497069
报告人简介：陈德汗，华中师范大学助理教授，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M3AS, Journal of Functional analysis, Journal of Differential Equations, Inverse Problems等国际知名刊物上发表论文10余篇。
报告摘要：This talk develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider the so- called oversmoothing state in the sense that the Tikhonov penalization is not able to capture the true solution regularity and leads to the infinite penalty value in the solution. We establish a vast extension of the Hilbertian convergence theory through the use of invertible sectorial operators from the holomorphic functional calculus and the prominent theory of interpolation scales in Banach spaces. Applications of the proposed theory involving l1, Bessel potential spaces, and Besov spaces are discussed.