Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1523-1535 |
| Number of pages | 13 |
| Journal | Nonlinearity |
| Volume | 30 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |
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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 journal › Article
TY - JOUR
T1 - Rigidity of critical points for a nonlocal Ohta-Kawasaki energy
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.
U2 - 10.1088/1361-6544/aa6167
DO - 10.1088/1361-6544/aa6167
M3 - Article
VL - 30
SP - 1523
EP - 1535
JO - Nonlinearity
JF - Nonlinearity
SN - 0951-7715
IS - 4
ER -