Rigidity of critical points for a nonlocal Ohta-Kawasaki energy

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers.
We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.
Original languageEnglish
Pages (from-to)1523-1535
Number of pages13
JournalNonlinearity
Volume30
Issue number4
DOIs
Publication statusPublished - 2017
Externally publishedYes

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rigidity
Rigidity
Free energy
Critical point
critical point
Energy
Radial Symmetry
Global Minimizer
energy
Perimeter
One Dimension
balls
Free Energy
Ball
free energy
Necessary
symmetry
Term

Cite this

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abstract = "We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers.We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.",
author = "Serena Dipierro and Matteo Novaga and Enrico Valdinoci",
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Rigidity of critical points for a nonlocal Ohta-Kawasaki energy. / Dipierro, Serena ; Novaga, Matteo ; Valdinoci, Enrico .

In: Nonlinearity, Vol. 30, No. 4, 2017, p. 1523-1535.

Research output: Contribution to journalArticle

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AU - Dipierro, Serena

AU - Novaga, Matteo

AU - Valdinoci, Enrico

PY - 2017

Y1 - 2017

N2 - We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers.We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.

AB - We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers.We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.

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DO - 10.1088/1361-6544/aa6167

M3 - Article

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SP - 1523

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JO - Nonlinearity

JF - Nonlinearity

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