Introduction to Free Boundary Problems
Geared to beginning and mid-stage grad students
July 20-21, 2024
Lecturer: Mariana Smit Vega Garcia
Course Description: In broad terms, free boundaries appear when the solution to a problem consists of a pair: a function (often satisfying a partial differential equation), and a set associated to this function. Two central issues in the study of free boundary problems are:
What is the optimal regularity of the solution?
How smooth is the free boundary?
We will learn tools, such as monotonicity formulas, that will allow us to investigate these questions.