Calculus of Variations and Geometric Measure Theory
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S. Dipierro - M. Novaga - E. Valdinoci

Rigidity of critical points for a nonlocal Ohta-Kawasaki energy

created by novaga on 25 Apr 2016


Submitted Paper

Inserted: 25 apr 2016
Last Updated: 25 apr 2016

Year: 2016


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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