| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 15 | |
| DOI | https://doi.org/10.1051/cocv/2019005 | |
| Published online | 09 January 2020 | |
Lower bound for the perimeter density at singular points of a minimizing cluster in ℝN★
1
Mathematisches Institut, Universität Leipzig,
Augustus Platz 10,
04109
Leipzig, Germany.
2
Scuola Internazionale Superiore di Studi Avanzati,
via Bonomea 265,
34136
Trieste, Italy.
* Corresponding author: mmarini@sissa.it
Received:
7
August
2018
Accepted:
18
January
2019
In this paper, we study the blow-ups of the singular points in the boundary of a minimizing cluster lying in the interface of more than two chambers. We establish a sharp lower bound for the perimeter density at those points and we prove that this bound is rigid, namely having the lowest possible density completely characterizes the blow-up.
Mathematics Subject Classification: 49Q05 / 49Q20 / 53A10
Key words: Isoperimetric problems / partitioning problems / minimal surfaces
© EDP Sciences, SMAI 2020
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