## S. Dipierro - M. Novaga - E. Valdinoci

# Rigidity of critical points for a nonlocal Ohta-Kawasaki energy

created by novaga on 25 Apr 2016

[BibTeX]

*Submitted Paper*

**Inserted:** 25 apr 2016

**Last Updated:** 25 apr 2016

**Year:** 2016

**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.

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