2022

The Analysis Autumn School 2022 will be held from October 17, 2022 to October 21, 2022 online via Zoom. We will record the lectures and upload afterwards. 

Xavier Cabré (ICREA & Universitat Politècnica de Catalunya. Barcelona)

Title: "On the regularity of stable solutions to reaction-diffusion elliptic equations"

Abstract:

The regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970's. It was initiated by a work of Crandall and Rabinowitz, motivated by the Gelfand problem in combustion theory. The theory experienced a revival in the mid-nineties after new progress made by Brezis and collaborators. I will present these developments, as well as a recent work, in collaboration with Figalli, Ros-Oton, and Serra, which finally establishes the regularity of stable solutions up to the optimal dimension 9. I will also describe a more recent paper of mine which provides full quantitative proofs of the regularity results.

Alessio Figalli (ETH Zurich, Zurich)

Title: "The obstacle problem"

Abstract:

The aim of this course is to discuss the regularity theory for the obstacle problem, starting from the most classical results and concluding with some of the most recent developments on the regularity of the free boundary.

Organizers: Yi Zhang (Chinese Academy of Science)  Yuan Zhou (Beijing Normal University)

You can find the schedule and the link to the meeting below: 

Here is the Lecture note of Prof. Xavier Cabre: