Continuity and density results for a one-phase nonlocal free boundary problem

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)1387-1428
Number of pages42
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume34
Issue number6
DOIs
Publication statusPublished - 2017
Externally publishedYes

Fingerprint Dive into the research topics of 'Continuity and density results for a one-phase nonlocal free boundary problem'. Together they form a unique fingerprint.

Cite this