A rigidity theorem for parabolic 2-Hessian equations
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- by Yan He, Cen Pan and Ni Xiang
- Proc. Amer. Math. Soc. 150 (2022), 3821-3830
- DOI: https://doi.org/10.1090/proc/15539
- Published electronically: June 16, 2022
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Abstract:
In this paper, we consider the entire solution to the parabolic $2$-Hessian equation $-u_t\sigma _2(D^2 u)=1$ in $\mathbb {R}^n\times (-\infty ,0]$. We prove a rigidity theorem for the parabolic $2$-Hessian equation in $\mathbb {R}^n\times (-\infty ,0]$ by establishing Pogorelov type estimates for $2$-convex-monotone solutions.References
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Bibliographic Information
- Yan He
- Affiliation: Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, People’s Republic of China
- MR Author ID: 919786
- ORCID: 0000-0002-0004-5642
- Email: helenaig@hotmail.com
- Cen Pan
- Affiliation: Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, People’s Republic of China
- Email: pancen960213@163.com
- Ni Xiang
- Affiliation: Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, People’s Republic of China
- Email: nixiang@hubu.edu.cn
- Received by editor(s): June 19, 2019
- Received by editor(s) in revised form: June 14, 2020, August 10, 2020, November 3, 2020, and January 9, 2021
- Published electronically: June 16, 2022
- Additional Notes: This research was supported by funds from the National Natural Science Foundation of China No. 11971157 and Hubei Provincial Department of Education Key Projects D20171004, D20181003.
The third author is the corresponding author. - Communicated by: Ryan Hynd
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3821-3830
- MSC (2020): Primary 35K55; Secondary 35B45
- DOI: https://doi.org/10.1090/proc/15539
- MathSciNet review: 4446232