Abstract
| 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 |
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Continuity and density results for a one-phase nonlocal free boundary problem. / Dipierro, Serena ; Valdinoci, Enrico .
In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 34, No. 6, 2017, p. 1387-1428.Research output: Contribution to journal › Article
TY - JOUR
T1 - Continuity and density results for a one-phase nonlocal free boundary problem
AU - Dipierro, Serena
AU - Valdinoci, Enrico
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
U2 - 10.1016/j.anihpc.2016.11.001
DO - 10.1016/j.anihpc.2016.11.001
M3 - Article
VL - 34
SP - 1387
EP - 1428
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
SN - 0294-1449
IS - 6
ER -