TY - JOUR

T1 - Gamma-convergence of nonlocal perimeter functionals

AU - Ambrosio, Luigi

AU - de Philippis, Guido

AU - Martinazzi, Luca

PY - 2011

Y1 - 2011

N2 - 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).

AB - 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).

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U2 - 10.1007/s00229-010-0399-4

DO - 10.1007/s00229-010-0399-4

M3 - Article

AN - SCOPUS:78751574089

VL - 134

SP - 377

EP - 403

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 3

ER -