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arXiv · 1711.07743

On The Phase Connectedness Of The Volume-Constrained Area Minimizing Partitioning Problem

Apostol Faliagas
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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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Apostol Faliagas. 2017-11-21. On The Phase Connectedness Of The Volume-Constrained Area Minimizing Partitioning Problem. https://doi.org/10.1007/s12220-017-9963-4

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