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Publication 16-CNA-013

On Periodic Critical Points And Local Minimizers Of The Ohta-Kawasaki Functional

Riccardo Cristoferi
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh PA 15213-3890 USA
rcristof@andrew.cmu.edu

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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