Uniqueness of the blow-down limit for triple junction problem

2024/04/03 by Zhiyuan Geng, Geng, Zhiyuan · 1 citation
Mathematics · #35A02 #35B08 #35J47 #35J50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.02859

openalex publication_date 2024/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the uniqueness of L¹ blow-down limit at infinity for an entire minimizing solution u:ℝ²→ℝ² of a planar Allen-Cahn system with a triple-well potential. Consequently, u can be approximated by a triple junction map at infinity. The proof exploits a careful analysis of energy upper and lower bounds, ensuring that the diffuse interface remains within a small neighborhood of the approximated triple junction at all scales.

Cited by

• Minimizing solutions of degenerate Allen-Cahn equations with three wells in ℝ²

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