※ 시간: 16:40-17:10
※ Zomm 병행: https://snu-ac-kr.zoom.us/j/2473239867
In this talk, I will introduce the regularity of the free boundary for the classical and double obstacle problems. Precisely, I will discuss the method of blowup to have the regularity of the free boundaries. Moreover, the difficulties from the existence of the two obstacles in the double obstacle problem will be introduced in the talk. The obstacle problems are typical examples of the free boundary problem and arise in porous media, elasto-plasticity, optimal control, and financial mathematics. In the last decades, many properties of the obstacle problems are studied by L. Caffarelli, K.-A. Lee, A. Figalli, H. Shahgholian, and various researchers. The double obstacle problem which is the problem with two obstacle functions arises in the study of option pricing with transaction costs, the game of tug-of-war, and semiconductor devices.