A Note Regarding Second-Order $\Gamma$-limits for the Cahn--Hilliard Functional

Abstract

This note completely resolves the asymptotic development of order $2$ by $\Gamma$-convergence of the mass-constrained Cahn--Hilliard functional, by showing that one of the critical assumptions of the authors' previous work (Leoni, Murray, Second-order $\Gamma$-limit for the Cahn--Hilliard functional, Arch. Ration. Mech. Anal. 219, 3, 2016) is unnecessary.