June 27, 10:00, Room 5.4 

This seminar focuses on the modern regularity theory via blow-up and compactness methods, and the main goal is to study three state-of-the-art papers. For the integro-differential obstacle problem, Caffarelli, Ros-Oton and Serra extended the regularity theory of free boundaries for the fractional Laplacian to a more general class of integro-differential operators. In the fully nonlinear setting, Savin and Yu developed fine estimates on the singular set of the obstacle problem for fully non-linear operators. Finally, in a very recent paper by Figalli, Ros-Oton, Serra we will see nonlocal obstacle problems with subcritical scaling due to a drift term; their results extend to the critical case and include the parabolic equation as well. A common feature of these three results is that they develop the regularity theory of the free boundary without the necessity of a monotonicity formula.

Schedule: To be announced

Organizers: Héctor Chang-Lara, Edgard Pimentel, Makson Santos 

More information at: https://www.mat.uc.pt/~hector.chang/obsprob25