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arXiv · 1901.11263

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

Changfeng Gui·Kelei Wang·Juncheng Wei
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Abstract

In this paper we study axially symmetric solutions of 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 $1$.

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Changfeng Gui, Kelei Wang, Juncheng Wei. 2019-01-31. Axially symmetric solutions of Allen-Cahn equation with finite Morse index. https://arxiv.org/abs/1901.11263

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