*Published Paper*

**Inserted:** 21 jul 2005

**Last Updated:** 4 apr 2016

**Journal:** Calc. Var. Partial Differential Equations

**Volume:** 26

**Number:** 4

**Pages:** 429-445

**Year:** 2006

**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.