Axially symmetric solutions of Allen-Cahn equation with finite Morse index
classification
🧮 math.AP
keywords
indexmorsesolutionsallen-cahnaxiallyendsequationfinite
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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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