Published Paper

Inserted: 4 dec 2024
Last Updated: 24 nov 2025

Journal: Adv. Calc. Var.
Volume: 18
Number: 4
Pages: 1301-1325
Year: 2025

Abstract:

We consider a variational model for heterogeneous phase separation, based on a diffuse interface energy with moving wells. Our main result identifies the asymptotic behavior of the first variation of the phase field energies as the width of the diffuse interface vanishes. This convergence result allows us to deduce a Gibbs-Thomson relation for heterogeneous surface tensions. Proceeding from this information, we prove that (weak) solutions of the Allen-Cahn equation with space dependent potential converge to a BV solution of weighted mean curvature flow, under an energy convergence hypothesis. Additionally, relying on the relative energy technique, we establish a weak-strong uniqueness principle for solutions of weighted mean curvature flow.