(Mini-Course) An introduction to Free boundary problems (IV)

地   点：  腾讯会议 APP3()

报告人：  Henrik Shagholian

单   位：  The Royal Institute of Technology (KTH), Sweden

邀请人：  李亚纯

备   注：  VooV Meeting Information (腾讯会议信息): Course time: 19:00-21:00 (GMT+08:00) China Stand Time-Beijing Each Tuesday from March 1 to March 22, 2022. Meeting ID: 550 2589 4725 Meeting Password: 123456 Click the link to join the meeting or to add it to your meeting list: https://meeting.tencent.com/dm/hQstEcGaBhxc

报告摘要：  

Abstract: In these lectures I shall cover some basic materials in free boundary problems, from various applications. These include problems from classical theory, as well as several new problems. The lectures will be at elementary level for both advanced master and Ph.D. students. Each lecture will be 2h, with a short break in between. The lectures will comprise the following moments:

1. What is a free boundary (examples from applications to modelling). 
I shall discuss several examples of free boundary problems, and the state of art for these problems. A few examples of such problems are: Ice melting, Hele-Shaw flow, Muskat problem, Control problem, Obstacle problem and their applications, Jets and Cavities,  scattering problems, Thin obstacle problem (nonlocal problem, with underlying levy process), and many others, if time allows  for the first lecture. The idea is to present a diverse range of problems, where free boundaries appear. 

2. Mathematical modelling of a few free boundary problems.
Some basics for mathematical modelling of several problems mentioned above will be introduced. 

3. Mathematical preliminaries for free boundary problems.
Several mathematical preliminaries for treating free boundary problems will be given, along with an over view to some tools. These include:  Variational problems, Viscosity solutions, Existence theory, 

4. Advanced theory: Soft approach to Regularity of solutions, and free boundaries. 
We shall expand further on the theory, introducing several advanced and modern tools, and using them for treatment of a few specific problems.

5. Open problems and future developments.
The participants will be introduced to several problems within the topic with exact ovulations and possible approaches, whenever there is one.