Axially symmetric solutions of the Allen-Cahn equation with finite Morse index

Axially symmetric solutions of the Allen-Cahn equation with finite Morse index

In this paper we study axially symmetric solutions of the Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between 4 and 10. In dimension 3, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly tw...

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Veröffentlicht in:Transactions of the American Mathematical Society 2020-05, Vol.373 (5), p.3649-3668
Hauptverfasser: Gui, Changfeng, Wang, Kelei, Wei, Jucheng
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Physical Sciences
Science & Technology
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Zusammenfassung:In this paper we study axially symmetric solutions of the Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between 4 and 10. In dimension 3, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals 1.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8035