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

Serena  Dipierro; Enrico  Valdinoci

doi:10.1016/j.anihpc.2016.11.001

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

Serena Dipierro, Enrico Valdinoci

Research output: Contribution to journal › Article

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 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	https://doi.org/10.1016/j.anihpc.2016.11.001
Publication status	Published - 2017
Externally published	Yes

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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 H{\"o}lder 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.",

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T1 - Continuity and density results for a one-phase nonlocal free boundary problem

AU - Dipierro, Serena

AU - Valdinoci, Enrico

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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 -