An optimal partition problem related to nonlinear eigenvalues

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Multipulse Phases in k-Mixtures of Bose–Einstein Condensates (2008, methodology): “This phenomenon, called “phase separation”, has been studied, starting from [4, 5], in the case of μi > 0 and in [3] in the case μi < 0, for least energy solutions in non necessarily symmetric bounded domains.”
NUMERICAL SIMULATIONS FOR NODAL DOMAINS AND SPECTRAL MINIMAL PARTITIONS (2010, unknown): “The following converse is deeper (see [HHO1], [CTV1, CTV2, CTV3] and [HHOT]) : Theorem 3.2 If the graph of the minimal partition is bipartite, this is the nodal partition of an eigen-function corresponding to L k (Ω) .”
On Spectral Minimal Partitions: A Survey (2010, methodology): “It has been proved by Conti-Terracini-Verzini [ CTV1 , CTV2, CTV3] (existence) and Helffer–Hoffmann-Ostenhof–Terracini [HHOT1] (regularity) the following theorem:”
Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case (2014, background): “1) when β → +∞ has firstly been studied in [11, 12] by Conti, Terracini and Verzini in the so-called focusing case ωi > 0: it has been shown that any sequence of minimizers of the energy functional associated to (1.”
The geometry of solutions to a segregation problem for nondivergence systems (2009, background): “This problem has received a considerable attention in particular [CTV][ CTV2 ] [CTV3][CTV4] vari-”