For the Allen-Cahn functional we study the following problem: for which prescribed amount m of volume is there the appearence of a droplet of one phase inside the other? Under a suitable assumption on the domain we show that the breaking of symmetry occurs at the same value of m as for the limit of the sharp interface energy. We also prove that there exists a threshold for m of order epsilon(n/n+1) so that either there is the appearence of the droplet or there is no breaking of symmetry.

Bellettini, G., Gelli, M., Luckhaus, S., Novaga, M. (2006). Deterministic equivalent for the Allen-Cahn energy of a scaling law in the Ising model. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 26(4), 429-445 [10.1007/s00526-006-0012-6].

Deterministic equivalent for the Allen-Cahn energy of a scaling law in the Ising model

BELLETTINI, GIOVANNI;
2006-01-01

Abstract

For the Allen-Cahn functional we study the following problem: for which prescribed amount m of volume is there the appearence of a droplet of one phase inside the other? Under a suitable assumption on the domain we show that the breaking of symmetry occurs at the same value of m as for the limit of the sharp interface energy. We also prove that there exists a threshold for m of order epsilon(n/n+1) so that either there is the appearence of the droplet or there is no breaking of symmetry.
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Bellettini, G., Gelli, M., Luckhaus, S., Novaga, M. (2006). Deterministic equivalent for the Allen-Cahn energy of a scaling law in the Ising model. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 26(4), 429-445 [10.1007/s00526-006-0012-6].
Bellettini, G; Gelli, M; Luckhaus, S; Novaga, M
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/37223
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