  We conduct an analysis of the blow up at the triple junction of three fluids
in equilibrium. Energy minimizers have been shown to exist in the class of
functions of bounded variations, and the classical theory implies that an
interface between two fluids is an analytic surface. We prove two monotonicity
formulas at the triple junction for the three-fluid configuration, and show
that blow up limits exist and are always cones. We discuss some of the
geometric consequences of our results.

Analysis of PDEs