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

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2026年2月17日

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Abhishek Adimurthi,
Peter Sternberg

摘要

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.