  We study the stability of partitions involving two or more phases in convex
domains under the assumption of at most two-phase contact, thus excluding in
particular triple junctions. We present a detailed derivation of the second
variation formula with particular attention to the boundary terms, and then
study the sign of the principal eigenvalue of the Jacobi operator. We thus
derive certain stability criteria, and in particular we recapture the
Sternberg-Zumbrun result on the instability of the disconnected phases in the
more general setting of several phases.
