On the Γ-convergence of the Allen-Cahn functional with boundary conditions

2023/01/18 by Dimitrios Gazoulis, Gazoulis, Dimitrios
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.07458

openalex publication_date 2023/01/18 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28

Abstract

We study minimizers of the Allen-Cahn system. We consider the ε -energy functional with Dirichlet values and we establish the Γ-limit. The minimizers of the limiting functional are closely related to minimizing partitions of the domain. Finally, utilizing that the triod and the straight line are the only minimal cones in the plane together with regularity results for minimal curves, we determine the precise structure of the minimizers of the limiting functional, and thus the limit of minimizers of the ε -energy functional as ε → 0 .

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