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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.
Paolini, Emanuele 1 ; Tamagnini, Andrea 1
@article{COCV_2018__24_3_1303_0,
author = {Paolini, Emanuele and Tamagnini, Andrea},
title = {Minimal clusters of four planar regions with the same area},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1303--1331},
publisher = {EDP-Sciences},
volume = {24},
number = {3},
year = {2018},
doi = {10.1051/cocv/2017066},
zbl = {1411.53013},
mrnumber = {3877203},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017066/}
}
TY - JOUR AU - Paolini, Emanuele AU - Tamagnini, Andrea TI - Minimal clusters of four planar regions with the same area JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1303 EP - 1331 VL - 24 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017066/ DO - 10.1051/cocv/2017066 LA - en ID - COCV_2018__24_3_1303_0 ER -
%0 Journal Article %A Paolini, Emanuele %A Tamagnini, Andrea %T Minimal clusters of four planar regions with the same area %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1303-1331 %V 24 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017066/ %R 10.1051/cocv/2017066 %G en %F COCV_2018__24_3_1303_0
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
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