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

Dario Reggiani

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arXiv · 2610.08485

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

Dario Reggiani

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Abstract

We establish a sharp comparison principle for the sharp-interface Ohta--Kawasaki energy and its Yukawa-screened counterpart in dimensions $2\le d\le5$, 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 $d\ge6$.

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Dario Reggiani. 2026-10-06. Global minimality of lamellae for isotropic Ohta--Kawasaki and Yukawa energies. https://arxiv.org/abs/2610.08485

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