Axially symmetric solutions of the Allen-Cahn equation with finite Morse index
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- by Changfeng Gui, Kelei Wang and Jucheng Wei PDF
- Trans. Amer. Math. Soc. 373 (2020), 3649-3668 Request permission
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 $1$.References
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Additional Information
- Changfeng Gui
- Affiliation: Department of Mathematics, University of Texas at San Antonio, San Antonio, Texas 78249; and School of Mathematics and Statistics, The Central South University, Changsha 410082, People’s Republic of China
- MR Author ID: 326332
- ORCID: 0000-0001-5903-6188
- Email: changfeng.gui@utsa.edu
- Kelei Wang
- Affiliation: School of Mathematics and Statistics & Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, People’s Republic of China
- MR Author ID: 866773
- ORCID: 0000-0002-2815-0495
- Email: wangkelei@whu.edu.cn
- Jucheng Wei
- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
- MR Author ID: 339847
- ORCID: 0000-0001-5262-477X
- Email: jcwei@math.ubc.ca
- Received by editor(s): February 3, 2019
- Received by editor(s) in revised form: February 28, 2019, and September 22, 2019
- Published electronically: February 19, 2020
- Additional Notes: The research of the first author was partially supported by NSF grant DMS-1601885.
The research of the second author was supported by NSFC. 11871381 and 11631011.
The research of the third author was partially supported by NSERC of Canada. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 3649-3668
- MSC (2010): Primary 35B53, 35J15, 35J20, 35J91, 53A05, 53A10
- DOI: https://doi.org/10.1090/tran/8035
- MathSciNet review: 4082251