On the regularity theory of the optimal switching problem

Abstract: The talk will begin with an overview of the obstacle problem in order to illustrate the main ideas and techniques in the theory of free boundary problems. Then we will study a weakly coupled system with interconnected obstacles arising in the optimal switching problem with two switching modes. We will discuss  the optimal regularity of solutions to the optimal switching problem, the relation to the double obstacle problem, and the regularity of the free boundary in dimension two.