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Rigidity of critical points for a nonlocal Ohta–Kawasaki energy.
- Source :
-
Nonlinearity . Apr2017, Vol. 30 Issue 4, p1-1. 1p. - Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09517715
- Volume :
- 30
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Nonlinearity
- Publication Type :
- Academic Journal
- Accession number :
- 121981583
- Full Text :
- https://doi.org/10.1088/1361-6544/aa6167