Abstract
We give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-116 |
| Number of pages | 116 |
| Journal | Memoirs of the American Mathematical Society |
| Volume | 249 |
| Issue number | 1181 |
| DOIs | |
| State | Published - Sep 2017 |
| Externally published | Yes |
Keywords
- Almgren's frequency formula
- Caffarelli's monotonicity formula
- Evolutionary variational inequality
- Free boundary problem
- Monneau's monotonicity formula
- Optimal regularity
- Parabolic Signorini problem
- Regularity of free boundary
- Singular set
- Weiss's monotonicity formula
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics