Regularity of Free Boundaries in Obstacle Problems - Lecture II

Delve into the second lecture of a series on free boundary problems in obstacle problems, exploring the regularity of free boundaries. Learn about the mathematical challenges in understanding these interfaces, which arise in various fields such as Physics, Geometry, Probability, Biology, and Finance. Examine the Stefan problem and the obstacle problem as classical examples, and discover the main known results in this context. Gain insights into current research and open problems in the field, utilizing methods from PDE, Calculus of Variations, and Geometric Measure Theory. This 56-minute lecture, presented by Xavier Ros-Oton at the Hausdorff Center for Mathematics, offers an in-depth look at the mathematical techniques used to study solutions and free boundaries in these complex problems.