Abstract
We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are Hölder continuous and the free boundary has positive density from both sides. For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.
| Original language | English |
|---|---|
| Pages (from-to) | 1387-1428 |
| Number of pages | 42 |
| Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
| Volume | 34 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |