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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2020

Half-space theorems for the Allen-Cahn equation and related problems

Résumé

In this paper we obtain rigidity results for a bounded non-constant entire solution u of the Allen-Cahn equation in R n , whose level set {u = 0} is contained in a half-space. If n ≤ 3 we prove that the solution must be one-dimensional. In dimension n ≥ 4, we prove that either the solution is one-dimensional or stays below a one-dimensional solution and converges to it after suitable translations. Some generalizations to one phase free boundary problems are also obtained.
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Dates et versions

hal-02184621 , version 1 (16-07-2019)
hal-02184621 , version 2 (27-07-2019)

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Citer

François Hamel, Yong Liu, Pieralberto Sicbaldi, Kelei Wang, Juncheng Wei. Half-space theorems for the Allen-Cahn equation and related problems. Journal für die reine und angewandte Mathematik, 2020, 770 (770), pp.113-133. ⟨10.1515/crelle-2020-0007⟩. ⟨hal-02184621v2⟩
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