The Singular Set in the Fully Nonlinear Obstacle Problem - Ovidiu Savin

Explore the intricacies of the fully nonlinear obstacle problem in this analysis seminar lecture delivered by Ovidiu Savin from Columbia University. Delve into the complexities of the singular set, beginning with an introduction to Caffarelli's work and the concept of free boundary. Examine the characteristics of singular points, with a focus on isolated points, and investigate the principles of monotonicity and unique limits. Learn about the monotonic formula and parametric inequality, and consider alternative approaches to the problem. Analyze the naive approach and explore full lines of singularities, concluding with a discussion on radially symmetric solutions. Gain valuable insights into this advanced mathematical topic through a comprehensive exploration of its key components and methodologies.

Intro
Caffarelli
The free boundary
Singular points
Isolated points
Monotonicity
Unique limits
Monotonic formula
Parametric inequality
A slightly different approach
The naive approach
Full line of singularities
Radially symmetric