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October 13, 2025Open Access

Minimizers of the Allen-Cahn energy with sub-quadratic growth

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We establish Liouville theorems for global minimizers of the allen-cahn energy, indicating implications for unbounded solutions.

Global minimizers of the Allen-Cahn energy exhibit subquadratic growth at infinity, showing significant behavior in unbounded settings.
These findings extend previously established results regarding De Giorgi's conjecture, enhancing the understanding of minimizers.
The analysis incorporates the regularity of minimizers for Dirichlet/perimeter functionals, providing a comprehensive framework.
Insights gathered from these Liouville theorems could influence future studies on phase transitions and related mathematical models.

Savin et al. (2025) studied this question.

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