no. 3
Minimal clusters of four planar regions with the same area
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1303-1331.

We prove that the optimal way to enclose and separate four planar regions with equal area using the less possible perimeter requires all regions to be connected. Moreover, the topology of such optimal clusters is uniquely determined.

DOI : 10.1051/cocv/2017066
Classification : 53A10, 49Q05, 52C99
Mots clés : Minimal clusters, planar networks
Paolini, Emanuele 1 ; Tamagnini, Andrea 1

1 
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Paolini, Emanuele; Tamagnini, Andrea. Minimal clusters of four planar regions with the same area. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1303-1331. doi : 10.1051/cocv/2017066. http://archive.numdam.org/articles/10.1051/cocv/2017066/

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