*Published Paper*

**Inserted:** 18 sep 2001

**Journal:** Proceedings of the Royal Society of Edinburgh

**Number:** 131A

**Pages:** 425-436

**Year:** 2001

**Abstract:**

In this paper we prove a certain regularity property of configurations of immiscible fluids, filling a bounded container $\Omega$ and locally minimizing the sum over $i<j$ of $c_{ij} \

S_{ij}\

$, where $S_{ij}$ represents the interface between fluid $i$ and fluid $j$, $\

\cdot \

$ stands for *area* or more general area-type functional, and $c_{ij}$ is a positive coefficient. More precisely, we show that, under *strict triangularity* of the $c_{ij}$'s, no *infiltrations* of other fluids are allowed between two main ones. A remarkable consequence of this fact is the almost-everywhere regularity of the interfaces. Our analysis is performed in general dimension $n> 1$ and with volume constraints on fluids.

**Keywords:**
Sets of finite perimeter, Immiscible fluids