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Axially symmetric solutions of the Allen-Cahn equation with finite Morse index.
- Source :
- Transactions of the American Mathematical Society; May2020, Vol. 373 Issue 5, p3649-3668, 20p
- Publication Year :
- 2020
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- MORSE theory
EQUATIONS
FINITE, The
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 373
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 142633693
- Full Text :
- https://doi.org/10.1090/tran/8035