Calculus of Variations and Geometric Measure Theory
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E. Paolini - A. Tamagnini

Minimal clusters of four planar regions with the same area

created by tamagnini on 20 Jul 2016
modified by paolini on 21 Feb 2018

[BibTeX]

Accepted Paper

Inserted: 20 jul 2016
Last Updated: 21 feb 2018

Journal: ESAIM: COCV
Year: 2018
Doi: 10.1051/cocv/2017066

ArXiv: 1612.00178v2 PDF

Abstract:

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.

Keywords: minimal cluster, bubbles


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