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Valdinoci, Enrico [Author]; Dipierro, Serena [Author]

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

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  • Media type: E-Article; Text
  • Title: Continuity and density results for a one-phase nonlocal free boundary problem
  • Contributor: Valdinoci, Enrico [Author]; Dipierro, Serena [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2017
  • Language: English
  • DOI: https://doi.org/10.1016/j.anihpc.2016.11.001
  • ISSN: 0294-1449 -- 49817-8 -- Annales de l'Institut Henri Poincaré C, Analyse non linéaire -- https://www.sciencedirect.com/journal/annales-de-linstitut-henri-poincare-c-analyse-non-lineaire
  • Keywords: article ; Free boundary problems -- nonlocal minimalsurfaces -- fractional operators -- regularity theory -- fractional harmonic replacement
  • Origination:
  • Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Description: 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.