OPTIMAL REGULARITY FOR SUPERCRITICAL PARABOLIC OBSTACLE PROBLEMS
Event details
| Date | 13.05.2022 |
| Hour | 14:15 |
| Speaker | Damià Torres-Latorre, Univ. Barcelona |
| Location | |
| Category | Conferences - Seminars |
Abstract. The nonlocal parabolic obstacle problem for an elliptic operator L with zero obstacle is
When L is the Laplacian, this problem is closely related to the Stefan problem, that models phase transitions. When L is a nonlocal operator such as the fractional laplacian (−∆)s, the equation serves as a model for stock pricing and other random processes with jumps.
The elliptic (time-stationary) version of this problem has been thoroughly studied since the pioneer works of Caffarelli, Salsa and Silvestre around 2007. However, much less is known about the parabolic problem.
When L is the fractional Laplacian, Caffarelli and Figalli proved in 2013 that the solutions are C1,s in space and C1,α in time. Still in the case of (−∆)s, for s > 1/2, Barrios, Figalli and Ros-Oton proved that the free boundary is C1,α at regular points.
In this talk, we present our recent results with X. Ros-Oton, where we proved the optimal regularity of the solutions and a global C1,α free boundary regularity
for the case s < 1/2 .
Practical information
- General public
- Free
Organizer
- Prof. Maria Colombo
Contact
- Prof. Maria Colombo