Work

Local minimizers in 3d of vector Allen-Cahn with a quadruple junction.

Year: 2026

Type: article

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.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-026-03252-1

Authors: Abhishek Adimurthi, Peter Sternberg

Institutions: Indiana University Bloomington, Indiana University

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Science Foundation, Simons Foundation, Division of Mathematical Sciences