Calculus of Variations and Geometric Measure Theory

R. Cristoferi

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

created by cristoferi on 16 Nov 2015
modified on 06 Aug 2018


Published Paper

Inserted: 16 nov 2015
Last Updated: 6 aug 2018

Journal: Nonlin. Anal.
Volume: 168
Pages: 81-109
Year: 2018


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.