Allen–Cahn solutions with triple junction structure at infinity
É Sandier, P Sternberg - Communications on Pure and Applied …, 2024 - Wiley Online Library
We construct an entire solution U : R 2 → R 2 $U:\mathbb {R}^2\rightarrow \mathbb {R}^2$
to the elliptic system Δ U = ∇ u W ( U ) , $$\begin{equation*} \Delta U=\nabla _uW(U), \end{equation*} …
to the elliptic system Δ U = ∇ u W ( U ) , $$\begin{equation*} \Delta U=\nabla _uW(U), \end{equation*} …
Uniqueness of the blow‐down limit for a triple junction problem
Z Geng - Communications on Pure and Applied Mathematics, 2025 - Wiley Online Library
We prove the uniqueness of L 1 L^1 blow‐down limit at infinity for an entire minimizing
solution u: R 2→ R 2 u:R^2→R^2 of a planar Allen–Cahn system with a triple‐well potential …
solution u: R 2→ R 2 u:R^2→R^2 of a planar Allen–Cahn system with a triple‐well potential …
Rigidity results for a triple junction solution of Allen-Cahn system
Z Geng - arXiv preprint arXiv:2412.02954, 2024 - arxiv.org
For the two dimensional Allen-Cahn system with a triple-well potential, previous results
established the existence of a minimizing solution $ u:\mathbb {R}^ 2\rightarrow\mathbb {R} …
established the existence of a minimizing solution $ u:\mathbb {R}^ 2\rightarrow\mathbb {R} …