Stable Free Boundaries in Dimension 3: Bernoulli and Allen--Cahn
Event details
| Date | 03.10.2025 |
| Hour | 14:15 |
| Speaker | Dr. Xavier Fernandez-Real (EPFL-AMCV) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
In this talk, I will present our recent work on the classification of global stable solutions to the Bernoulli problem in $\mathbb R^3$. In particular, this yields local universal curvature bounds for the free boundary for the local problem.
By means of this result, we prove the free boundary Allen--Cahn stability conjecture in dimension 3: global stable solutions to the free boundary analogue of the Allen--Cahn equation are one dimensional in dimension 3. This solves the long-standing De Giorgi conjecture in the free boundary case.
Practical information
- General public
- Free
Organizer
- Prof. Maria Colombo
Contact
- Prof. Maria Colombo