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 |
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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 |