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• W4309582787 abstract "Abstract The seminal results of Bourgain et al. (Optimal Control and Partial Differential Equations, IOS, Amsterdam, 2001) and Dávila (Calc Var Partial Differ Equ 15(4):519–527, 2002) show that the classical perimeter can be approximated by a family of nonlocal perimeter functionals. We consider a corresponding second order expansion for the nonlocal perimeter functional. In a special case, the considered family of energies is also relevant for a variational model for thin ferromagnetic films. We derive the $$Gamma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Γ</mml:mi> </mml:math> –limit of these functionals as $$epsilon rightarrow 0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>→</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . We also show existence for minimizers with prescribed volume fraction. For small volume fraction, the unique, up to translation, minimizer of the limit energy is given by the ball. The analysis is based on a systematic exploitation of the associated symmetrized autocorrelation function." @default.
• W4309582787 created "2022-11-28" @default.
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• W4309582787 date "2022-11-19" @default.
• W4309582787 modified "2023-09-24" @default.
• W4309582787 title "Second Order Expansion for the Nonlocal Perimeter Functional" @default.
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• W4309582787 doi "https://doi.org/10.1007/s00220-022-04549-w" @default.
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