| Autor: |
Hamel, François, Liu, Yong, Sicbaldi, Pieralberto, Wang, Kelei, Wei, Juncheng |
| Předmět: |
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| Zdroj: |
Journal für die Reine und Angewandte Mathematik; 2021, Vol. 2020 Issue 769, p113-133, 21p |
| Abstrakt: |
In this paper we obtain rigidity results for a non-constant entire solution u of the Allen–Cahn equation in ℝn, 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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