Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem

We develop a rigorous numerical method to compare local minimizers of the Ohta–Kawasaki functional in two dimensions. In particular, we validate the phase diagram identifying regions of parameter space where rolls are favorable, where hexagonally packed spots have lowest energy and finally where the constant mixed state does. More generally, we present a method to rigorously determine such features in problems where optimal domain sizes are not known a priori.