Infiltrations in immiscible fluids systems

In this paper we prove a certain regularity property of configurationsof immiscible fluids, filling a bounded container and locally minimizingthe interface energyPi<j cijkSijk, where Sij represents the interfacebetween fluid i and fluid j, k · k stands for area or more general area-type functional, and cij is a positive coefficient. More precisely, we showthat, under strict triangularity of the cij ’s, no infiltrations of other fluidsare allowed between two main ones. A remarkable consequence of thisfact is the almost-everywhere regularity of the interfaces. Our analysisis performed in general dimension n ≥ 2 and with volume constraintson fluids.