Global minimality of lamellae for isotropic Ohta--Kawasaki and Yukawa energies

We establish a sharp comparison principle for the sharp-interface Ohta–Kawasaki energy and its Yukawa-screened counterpart in dimensions $2\le d\le 5$, for $m=0$, and under periodic and zero-flux Neumann boundary conditions. Whenever the finite optimal stripe width is compatible with the domain, we prove global minimality of periodic lamellae and characterize all minimizers. The proof combines a positive radial comparison measure, a sharp Fourier bound, and rigidity for a directional translation inequality in $BV$. We also identify an obstruction to this measure construction in dimensions $d\ge 6$.