On the Phase Connectedness of the Volume-Constrained Area Minimizing
Partitioning Problem
Abstract
We study the stability of partitions in convex domains involving simultaneous
coexistence of three phases, viz. triple junctions. We present a careful
derivation of the formula for the second variation of area, written
in a suitable form with particular attention to boundary and spine
terms, and prove, in contrast to the two phase case, the existence
of stable partitions involving a disconnected phase.