Local minimizers in 3d of vector Allen-Cahn with a quadruple junction.
Abstract
Abstract For $$\Omega $$ Ω a perturbation of the unit ball in $$\mathbb {R}^3$$ R 3 , we establish the existence of a sequence of local minimizers for the vector Allen-Cahn energy. The sequence converges in $$L^1$$ L 1 to a partition of $$\Omega $$ Ω whose skeleton is given by a tetrahedral cone and thus contains a quadruple point. This is accomplished by proving that the partition is an isolated local minimizer of a weighted perimeter problem arising as the associated $$\Gamma $$ Γ -limit of the sequence of Allen-Cahn functionals.
Fields of Study & Subjects
Solidification and crystal growth phenomena
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 3
- Publication date
- 17 February 2026
- Language
- EN