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
SN - 0025-2611
VL - 134
SP - 377
EP - 403
JO - manuscripta mathematica
JF - manuscripta mathematica
IS - 3
ER -