课程题目：Regularization and discretization issues in the reconstruction for elliptic inverse problems

授课人： Luca Rondi

所在单位：Università di Pavia

授课时间：2026年07月21、22、23日

授课地点：正新楼313教室

课程介绍:

    We discuss the variational approach to the reconstruction for elliptic inverse problems such as the electrical impedance tomography or the determination of inhomogeneities by scattering measurements. When approaching the reconstruction for inverse problems, two of the main difficulties one has to face are nonlinearity and ill-posedness. In fact, most inverse problems are ill-posed, that is, they lack stability. For elliptic inverse problems, the ill-posedness, or instability, is severe or exponential making the reconstruction particularly challenging. To deal with the ill-posedness, some kind of regularization is required which, in the variational approach, is often of Tikhonov type. The discretization used for the numerical implementation may be another important cause of instability, which is often overlooked. We investigate how to handle simultaneously the regularization and the discretization so that the solution to the corresponding regularized and discrete minimization problem is a good approximation of the looked-for solution to the inverse problem.

授课人简介：

   Luca Rondi graduated in Mathematics at the Università di Trieste in 1996 and obtained his Ph.D. in Mathematics at SISSA, Trieste, in 1999 under the supervision of Professor Giovanni Alessandrini. From November 1999 till June 2000, he was a postdoc research assistant at Johannes Kepler University of Linz, Austria. During the academic year 2000-2001, he was a Dunham Jackson Assistant Professor at the University of Minnesota, Minneapolis, USA. From September 2001 till December 2012, he was Assistant Professor in Mathematical Analysis at the Università di Trieste. Since December 2012 he has been Associate Professor in Mathematical Analysis, at the Università di Trieste till September 2018, at the Università di Milano till April 2021, and at the Università di Pavia from May 2021. He held long visiting position at the University of Minnesota, Minneapolis (2007 Fall term) and at MSRI, Berkeley, USA (one month in 2010). His fields of research are partial differential equations, with a particular focus on inverse problems, Calculus of Variations and imaging. He has been a member of the Editorial Board of the journal “Communications on Analysis and Computation” (CAC) since its inception in 2023.

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