Coincidence criteria and junction obstructions for two partially segregated elliptic systems

We compare two singularly perturbed elliptic systems with the same partial-segregation constraint but different limiting mechanisms. System~A is determined by harmonic-difference identities and admits an explicit lower-envelope limit, whereas System~B converges, along subsequences, to a constrained Dirichlet-energy minimizer. We show that the System~A profile need not be stationary for the limiting variational problem. We establish conditional coincidence criteria, give explicit data for which the interfaces differ, and derive a planar triple-junction obstruction. In particular, coincidence with the standard variational cone requires the triangle formed by the harmonic gradients to be equilateral. This condition is necessary but not sufficient.