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.
Continuity and density results for a one-phase nonlocal free boundary problem
E Valdinoci
2017
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.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
prod_367473-doc_130842.pdf
solo utenti autorizzati
Descrizione: Continuity and density results for a one-phase nonlocal free boundary problem
Tipologia:
Versione Editoriale (PDF)
Dimensione
596.93 kB
Formato
Adobe PDF
|
596.93 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
