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.
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Faliagas, A.C. On the Phase Connectedness of the Volume-Constrained Area Minimizing Partitioning Problem. J Geom Anal 28, 3373–3423 (2018). https://doi.org/10.1007/s12220-017-9963-4
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DOI: https://doi.org/10.1007/s12220-017-9963-4