Year: 2026
Type: preprint
Abstract: We study bounded entire solutions of the Allen-Cahn equation in dimension three with quadratic energy growth. We prove that such a solution of finite Morse index I has at most 2I ends. Furthermore, we show that Morse index one solutions have two ends and are axially symmetric, which generalizes an earlier result by Florit-Simon.
Source: arXiv (Cornell University)
Authors: Liu, Yong, Wang, Kelei, Wei, Juncheng, Wu, Ke
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G17982248, G5208386829, G7833826364
OpenAlex ID: W7213352653