Free Boundary Problems
Real Analysis (graduate), Partial Differential Equations (recommended)
This course will serve as an introduction to the modern theory of free boundary problems, with an emphasis on the regularity of the interface. We will discuss the traditional Bernoulli and obstacle-type problems, as well as thin or fractional variants and some applications to shape optimization. We will also highlight connections to geometric measure theory and minimal surfaces, especially in relation to the structure of singularities.