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arXiv · 2601.05682

Coincidence criteria and junction obstructions for two partially segregated elliptic systems

Farid Bozorgnia
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Abstract

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.

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Farid Bozorgnia. 2026-01-09. Coincidence criteria and junction obstructions for two partially segregated elliptic systems. https://arxiv.org/abs/2601.05682

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