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arXiv · 1606.05315

Global minimizers of the Allen-Cahn equation in dimension $n\geq 8$

Yong Liu·Kelei Wang·Juncheng Wei
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Abstract

We prove the existence of global minimizers of Allen-Cahn equation in dimensions $8$ and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global minimizers whose nodal sets are asymptotic to the cones. As a consequence of Jerison-Monneau's program we establish the existence of many counter-examples to the De Giorgi's conjecture different from the Bombierie-De Giorgi-Giusti minimal graph.

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Yong Liu, Kelei Wang, Juncheng Wei. 2016-06-16. Global minimizers of the Allen-Cahn equation in dimension $n\geq 8$. https://arxiv.org/abs/1606.05315

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