Lower bound for the perimeter density at singular points of a minimizing cluster in $\mathbb{R}^N$

Hirsch, Jonas; Marini, Michele

doi:10.1051/cocv/2019005

Lower bound for the perimeter density at singular points of a minimizing cluster in

ℝ^{N}

Hirsch, Jonas ; Marini, Michele

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 1.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

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.

MR Zbl

DOI : 10.1051/cocv/2019005

Classification : 49Q05, 49Q20, 53A10
Mots-clés : Isoperimetric problems, partitioning problems, minimal surfaces

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     author = {Hirsch, Jonas and Marini, Michele},
     title = {Lower bound for the perimeter density at singular points of a minimizing cluster in $\mathbb{R}^N$},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2019005},
     mrnumber = {4049314},
     zbl = {1439.49073},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2019005/}
}

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Hirsch, Jonas; Marini, Michele. Lower bound for the perimeter density at singular points of a minimizing cluster in $\mathbb{R}^N$. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 1. doi : 10.1051/cocv/2019005. http://www.numdam.org/articles/10.1051/cocv/2019005/

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Cité par Sources :

The work of the authors is supported by the MIUR SIR-grant “Geometric Variational Problems” (RBSI14RVEZ).