Infiltrations in immiscible fluids systems

In this paper we prove a certain regularity property of configurations of immiscible fluids, filling a bounded container R and locally minimizing the interface energy Sigma (i <j) c(ij) //S-ij//, where S-ij represents the interface between fluid i and fluid j: // . // 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), 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 greater than or equal to 2 and with volume constraints on fluids.