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

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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 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

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Free Boundary Problem
Fractional
Perimeter
Free Boundary
Minimizer
Dirichlet
Superposition
Replacement
Harmonic
Energy

Cite this

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title = "Continuity and density results for a one-phase nonlocal free boundary problem",
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.",
author = "Serena Dipierro and Enrico Valdinoci",
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T1 - Continuity and density results for a one-phase nonlocal free boundary problem

AU - Dipierro, Serena

AU - Valdinoci, Enrico

PY - 2017

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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 -