Calculus of Variations and Geometric Measure Theory
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R. Cristoferi

On periodic critical points and local minimizers of the Ohta-Kawasaki functional

created by cristoferi on 16 Nov 2015
modified on 22 Nov 2016

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Inserted: 16 nov 2015
Last Updated: 22 nov 2016

Year: 2015

Abstract:

In this paper we collect some new observations about periodic critical points and local minimizers of a nonlocal isoperimetric problem, arising in the modeling of diblock copolymers. In the main result, by means of a purely variational procedure, we show that it is possible to construct (locally minimizing) periodic critical points whose shape resemble that of any given strictly stable constant mean curvature (periodic) hypersurface. Along the way, we establish several auxiliary results of independent interest.


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