Gamma-convergence of nonlocal perimeter functionals

Luigi Ambrosio, Guido de Philippis, Luca Martinazzi

Research output: Contribution to journalArticlepeer-review

Abstract

Given Ω ⊂ Rn open, connected and with Lipschitz boundary, and s ε (0, 1), we consider the functional, where E ⊂ Rn is an arbitrary measurable set. We prove that the functionals (1-s)Js(·,Ω) are equi-coercive in Lloc1(Ω) as s ↑ 1 and that, for every E ⊂ Rn measurable, where P(E,Ω) denotes the perimeter of E in Ω in the sense of De Giorgi. We also prove that as s ↑ 1 limit points of local minimizers of (1-s)Js(.,Ω) are local minimizers of P(·,Ω).

Original languageEnglish (US)
Pages (from-to)377-403
Number of pages27
Journalmanuscripta mathematica
Volume134
Issue number3
DOIs
StatePublished - 2011

ASJC Scopus subject areas

  • Mathematics(all)

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