The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3373–3423 | Cite as

On the Phase Connectedness of the Volume-Constrained Area Minimizing Partitioning Problem

  • A. C. FaliagasEmail author


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.


Area minimizer Phase connectedness Triple junction Second variation Phase coexistence Volume constraints 

Mathematics Subject Classification

53C42 49Q10 53A10 58J50 


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Copyright information

© Mathematica Josephina, Inc. 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Athens, PanepistemiopolisAthensGreece

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